Did Russia tamper with any votes or the vote counting process?

Apparently not. The outgoing Obama administration insisted that the voting process was free of interference. Officials in the Obama White House later reported that they were very concerned about that possibility prior to election day, and that a big part of their response to Russia's activities was focused on preventing any vote tampering. According to the declassified intelligence report, while "Russian intelligence obtained and maintained access to elements of multiple US state or local electoral boards. DHS assesses that the types of systems Russian actors targeted or compromised were not involved in vote tallying." A recount of the vote in Wisconsin found no evidence of tampering. 

What did Russia hope to accomplish?

According to testimony in the Senate Intelligence Committee hearings, "Russia certainly seeks to promote Western candidates sympathetic to their worldview and foreign policy objectives. But winning a single election is not their end goal. Russian Active Measures hope to topple democracies through the pursuit of five complementary objectives:

• Undermine citizen confidence in democratic governance
• Foment and exacerbate divisive political fractures
• Erode trust between citizens and elected officials and democratic institutions
• Popularize Russian policy agendas within foreign populations
• Create general distrust or confusion over information sources by blurring the lines between fact and fiction

From these objectives, the Kremlin can crumble democracies from the inside out creating political divisions resulting in two key milestones: 1) the dissolution of the European Union and 2) the break up of the North American Treaty Organization (NATO). Achieving these two victories against the West will allow Russia to reassert its power globally."

(As a candidate Donald Trump called NATO "obsolete", and supported Britain's exit ("Brexit") from the EU. He also supported the French presidential candidate who wanted France to leave the European Union.)

The CIA, NSA, and FBI have said that "The Kremlin sought to advance its longstanding desire to undermine the US-led liberal democratic order, the promotion of which Putin and other senior Russian leaders view as a threat to Russia and Putin’s regime." In service of these goals, they say, "Putin and the Russian Government aspired to help President-elect Trump’s election chances when possible by discrediting Secretary Clinton and publicly contrasting her unfavorably to him," but "When it appeared to Moscow that Secretary Clinton was likely to win the election, the Russian influence campaign began to focus more on undermining her future presidency."

Finally, the same declassified intelligence report states that: "Putin most likely wanted to discredit Secretary Clinton because he has publicly blamed her since 2011 for inciting mass protests against his regime in late 2011 and early 2012, and because he holds a grudge for comments he almost certainly saw as disparaging him."

If they didn't tamper with votes, in what ways DID they interfere with the election?

From the declassified intelligence report: "The Kremlin’s campaign aimed at the US election featured disclosures of data obtained through Russian cyber operations; intrusions into US state and local electoral boards; and overt propaganda."

These"cyber operations" included "targets associated with both major US political parties. We assess Russian intelligence services collected against the US primary campaigns, think tanks, and lobbying groups they viewed as likely to shape future US policies. In July 2015, Russian intelligence gained access to Democratic National Committee (DNC) networks and maintained that access until at least June 2016." The DNC hired a security firm called CrowdStrike, who were able to watch the hackers in action. Stolen files were released to the public through Wikileaks and DC leaks.

Hackers also targeted election systems in over 20 states, though the report says those systems were not involved in tabulating votes. Some were databases of voter registration and related information. According to NBC news: "Only two successful breaches have been disclosed, both of online voter registration databases, in Illinois and Arizona over the summer. While those two hacks were linked to hackers in Russia, the DHS official did not say who was responsible for the other failed attempts, noting that 'we're still doing a lot of forensics.'"

According to ABC News: "Dr. Andy Ozment, the assistant secretary for cybersecurity and communications at DHS, told lawmakers on Wednesday [Sept 28,2016] that the hackers who broke into the voter registration system in Illinois and targeted a similar system in Arizona appear to have been looking to copy the personal information in those databases and perhaps then sell that information online."

In retrospect it seems likely that the aim was not to sell this information, but to provide data to help Russian propaganda target Americans on social media.  According to the declassified report the Russian propaganda network  RT (formerly "Russia Today"): "is making its social media operations a top priority.[...] RT's website receives at least 500,000 unique viewers every day. Since its inception in 2005, RT videos received more than 800 million views on YouTube (1 million views per day), which is the highest among news outlets." By contrast the report says CNN has received less than 100 million views YouTube in the same period, and has 150 million subscribers to its YouTube Channel, to RT's 450 million.

The report also says that Russia used fake social media accounts operated by paid "trolls" to spread rumors and amplify stories from their propaganda operations. "Russia used trolls as well as RT as part of its influence efforts to denigrate Secretary Clinton. This effort amplified stories on scandals about Secretary Clinton and the role of WikiLeaks in the election campaign. The likely financier of the so-called Internet Research Agency of professional trolls located in Saint Petersburg is a close Putin ally with ties to Russian intelligence. A journalist who is a leading expert on the Internet Research Agency claimed that some social media accounts that appear to be tied to Russia’s professional trolls—because they previously were devoted to supporting Russian actions in Ukraine—started to advocate for President-elect Trump as early as December 2015."

Did Russian activities change the outcome of the election?

We will probably never know for sure.

Trump won  Michigan, Pennsylvania and Wisconsin by 0.2, 0.7 and 0.8 percentage points, respectively — by 10,704, 46,765 and 22,177 votes. Had he lost those three races, he would have lost the electoral college. These margins are small enough that all kinds of relatively small effects could in theory have changed the results one way or another. But we cannot measure exactly what reasons caused which voters to vote as they did, or to stay home.

We do know, however, that "Russia had every ability to create fake social media accounts by mimicking profiles of voters in key election states and precincts in the 2016 election, and use a mix of bots and real people to push propaganda from state-controlled media outlets like Russia Today (RT) and Sputnik [...] Clinton Watts, a senior fellow at the Center for Cyber and Homeland Security at The George Washington University, said many social accounts during the election pushing questionable news looked just like real voters in states like Wisconsin and Michigan." (From a CBS report on Senate Intelligence Committee testimony.)

Is there evidence that Trump or his campaign did anything illegal?

This is for the court system to decide, after an investigation. However, there are several actions we know about which could be found to have violated the law:

Trump firing FBI Director James Comey because he was frustrated with the FBI investigation of the election could be a violation of  laws against obstruction of justice.

Lying on security clearance forms, as Jeff Sessions and Jared Kushner and Michael Flynn appear to have done, is against the law, and so is lying under oath, as Sessions appears to have done in his confirmation hearing. Lying to the FBI in an interview, as Michael Flynn appears to have done, is also illegal. In all of these cases, the apparent lies concerned whether the individuals in question had contact with Russian officials. We say they "appear to" have lied because, while we know the statements they made were false, making false statements is only a "lie" and illegal in these contexts if they knew that the statements were false. This is the part a court will need to decide.

Jared Kushner's attempts to set up a covert communications channel to Moscow through the Russian embassy may violate laws against espionage.

The discussions of former National Security Advisor Michael Flynn with the Russian ambassador during the transition could violate the Logan Act, which forbids private citizens (which Flynn was at the time) from negotiating with foreign powers, but no one has ever been prosecuted for breaking that law.

Finally, suits have been brought asserting that the Trump administration is in violation of the "emoluments clause" of the constitution, which forbids US government officials from accepting payments from foreign governments.

Trump or his campaign team could potentially be charged with additional crimes depending on the outcome of the ongoing investigations. Subpoenas have been issued for the records of Michael Flynn and Paul Manafort, so far. 

Is there any evidence that Trump or his campaign colluded with Russia?

It depends on what you mean by "collusion." There is no crime called "collusion," and the word does not have a legal definition. We know that Trump mentioned the WikiLeaks releases over a hundred times in the final weeks of the campaign. He said he hoped Russia had hacked Hillary Clinton's e-mail account from her time as Secretary of State and called on them to release whatever they had, even as he denied Russian involvement in the hacking of the DNC.

And while we don't know what they said to each other, we do know that the Trump campaign had an unusual amount of contact with Russian officials during the run up to the election. As mentioned in the section above, several members of the Trump campaign and administration appear to have attempted to conceal those contacts: omitting them on security clearance forms, in Senate testimony, and in discussions with the FBI.

We also know that Acting Attorney General Sally Yates testified that she warned the Trump administration that Michael Flynn could be blackmailed by Russia because he had lied about what he discussed with them during the transition. The Russians knew the truth, and could threaten expose it. However, Flynn remained in office for 18 days, until after these lies were exposed by the US media. This suggests that the Trump administration apparently did not object to having someone they had been warned was compromised by Russia at the highest levels of White House staff, until the public outcry caused Flynn to resign.

We know that the day after FBI Director James Comey was fired, Trump casually shared highly classified intelligence with the Russian ambassador and foreign minister in the oval office. He did this without permission from the foreign ally which provided that intelligence. Trump's willingness to share sensitive information like this seems to offer evidence of a much closer relationship than would be expected given major disagreements with Russia about their invasions of Ukraine and Georgia, and support for Bashar al Assad in Syria.

There is, of course, plenty of evidence that Putin orchestrated a hacking and propaganda campaign to help Trump get elected.

Finally, Trump himself and the Trump administration as a whole has unusually close personal and financial ties to Russia.

None of this is proof that Trump or anyone in his campaign knew in advance that the Kremlin planned to hack the DNC or helped shape the messages of its propaganda campaign. Federal investigators are still looking into those questions. There is, however, considerable evidence of an unusually close relationship between the Trump campaign and the Russian government.

Is Russia planning to interfere in future elections?

Almost certainly. They already are in Germany: "After all, last year the same hackers who broke into the Democratic Party’s computers, known online as Fancy Bear or Sofacy Group, attacked the German Parliament’s network; they are also accused of stealing documents from individual members of Parliament." Some of the same social media accounts that supported Trump are now attacking Angela Merkel

They also attacked French presidential candidate Emmanuel Macron. Macron said:“During the campaign, Russia Today and Sputnik were agents of influence which on several occasions spread fake news about me personally and my campaign. [...] They behaved like organs of influence, of propaganda and of lying propaganda." Russia may have been involved in a leak of e-mails stolen from Macron's campaign.

And as recently as March, 2017, experts "observed possibly fake social media accounts discrediting Speaker of the House Paul Ryan [...] as the health care bill collapsed."

Disinformation, propaganda, and cyberwarfare are going to be threats to democratic governments around the world for the forseeable future.