There's a lot to look at but some important things to know above all else:
-Russia and US have been tentative allies at absolute best and have been ready to blow each other off the planet at worst. United States has pretty much always considered Russia as a "hostile" state. This includes now.
-It's been confirmed by every major intelligence agency we have that has reviewed the events leading up to and during the election that Russia hacked and influenced the 2016 presidential election. They have also been confirmed to have hacked into Facebook and Twitter and spreading mass disinformation, primarily to help Trump during the election.
-Putin is right wing. Only makes sense that he/oligarchs he's affiliated with would try to influence our own right wing politicians if he were to do such a thing. Which he did. The NRA base is like 3/4 conservative and they've been a powerful political organization for a minute now. They pump a lot of money into GOP senator's election campaigns (depending on who you are, millions of dollars), so by default that makes them one of the most influential right wing PACs out there. It only makes sense that Russia, if they were to try to influence American politics, would follow the money.
-While running for president and since becoming president, Trump has made a number of claims as far as all of this goes. He primarily blames Obama and the US intelligence agencies for either lying about Trump's ties to Russia or failing to stop Russia from hacking our election. Has basically deflected any blame that would be put on Russia.
It goes deeeeeeeeeeep. Like you and I probably won't ever know the full story deep. Actually we definitely won't considering how much sensitive/classified info is likely involved. Watergate is like the closest thing we have to it; that ended in about 40 people going to jail and Nixon and his VP resigning after about a two year investigation. We're roughly a year and a half to two years deep (since intelligence communities and the Obama presidency had been looking at Russia during the election) and Mueller and his legal team is probably looking at the following people/groups at minimum (some have already been arrested/looked at/otherwise processed):
Honestly I can hardly provide any info so I would highly recommend looking on Wikipedia and/or Reddit for more details on who these people are and what their relation to the investigation is if you're interested
*People related to Trump's campaign*
-Mike Pence, Vice President of the United States, presumably knows about Flynn's meeting with Russian ambassador Sergey Kislyak
-Paul Manafort, former Trump campaign manager and close associate for decades, (has since been arrested for illegal financial dealings in Ukraine)
-Carter Page, former Trump campaign manager and weird guy
-Corey Lewandowski, former Trump campaign manager
-Kellyanne Conway, former Trump campaign manager
-Reince Priebus, former chairman of the RNC and White house Chief of Staff, was key in trying to connect Trump to Ryan, McConnell and the legislative branch
-Rick Gates, former Trump campaign chairman (has since been arrested)
-Roger Stone, Trump adviser, confirmed to have communicated with hacker Guccifer 2.0 and could potentially be indicted by Mueller soon
-Michael Flynn, former National Security Adviser, lied to FBI agents about meeting with Russian ambassador Sergey Kislyak
-Jared Kushner, son-in-law of POTUS, has confirmed met with Russians during the campaign, has shady ties to China and the Middle East
-Steve Bannon, former chief strategist, member of the National Security Council, founding member of Breitbart and Cambridge Analytica
-Felix Sater, lifelong criminal mobster who had communicated with Putin's personal assistant about helping Donald Trump get elected with Russia's help. Has since been cooperating with investigators about a money laundering scheme that as far as I know isn't really related to the investigation
-Michael Cohen, former Trump attorney (recently raided by FBI)
-Jeff Sessions, Attorney General who has met with high ranking members of the Russian government like Sergey Kislyak (has recused himself from anything related to the investigation, hasn't revealed what he knows in Congressional hearings)
-George Papadopolous, former member of Trump's foreign advisory panel, has confirmed had email correspondence with Russians about apparent dirt on Hillary Clinton. Has been arrested for lying to FBI agents and is currently cooperating with Mueller's team.
-Alex van der Zwaan, has worked with Rick Gates and Paul Manafort's lobbying campaign for a Russian associate of Manafort's and has repeatedly helped Russian lobbyists improve assets. Charged with lying to FBI agents about his work with Gates and Manafort and has since been arrested, released, and deported to the Netherlands.
-Betsy DeVos, Trump's education secretary, part of billionaire family and related to Erik Prince
-George Nader, convicted pedo and key figure in setting up backchannels between the Middle East and the United States.
-Rudy Giuliani, cross-dresser and Trump's current attorney
-Hope Hicks, former Communications Director for President Trump. Had previously testified before a House committee that she had "told white lies" for Trump.
-Rex Tillerson, former Secretary of State. Has confirmed to have ties with Vladimir Putin and the Russian oil industry since his days as CEO of Exxon Mobil and opposed the sanctions against Russia. He also has ties to the Middle East.
-Gary Cohn, former Director of the National Economics Council.
-H.R. McMaster, former National Security Adviser. Was forced out in part due to his disagreements with Trump on his stances towards
-Scott Pruitt, former EPA head. Had a number of ethics scandals and was investigated by the House Oversight Committee for his outrageous spending of taxpayer money.
*Politicians and intelligence agency members*
-Mitch McConnell, senate GOP leader. Has hinted that he believes Russia hacked the election but has thus far opposed any legislation protecting Mueller and has called for it to end
-Paul Ryan, Speaker of the House. Has allegedly discussed laundering Russian money thru super PACs with McConnell. Isn't seeking re-election for unknown reasons.
-Devin Nunes, Chairman of the House Intelligence Committee and former member of Trump transition team. Was in hot water a while back for going to the White House and then leaking information about people in intelligence agencies keeping tabs on some people in the Trump team (which is classified info). Has been highly partisan and close with the White House since.
-James Comey, former FBI director who was fired by Trump in May 2017. Trump claims that at the recommendation of Sessions and Rosenstein, he fired Comey for his behavior related to the Russia investigation. Comey has since turned over memos relating to meetings with Trump and any relevant information he has.
-James Clapper, former Director of National Intelligence (has already testified to Congress)
-John Brennan, former CIA Director (has already testified to Congress)
-Rod Rosenstein, Deputy Attorney General who appointed Mueller to head the investigation. Likely has already been working closely with Mueller and Justice dept.
-Andrew McCabe, former Deputy FBI Director who was fired in March. He has had key roles in investigating both the Hillary Clinton email investigation and the Trump-Russia investigation
-Chris Wray, acting FBI Director
-Jill Stein, third party member who ran in 2016. She has been confirmed to have met with Russian higher-ups so if she were to be questioned she would be questioned about that as well as her misuse of campaign funds
And honestly there are a number of FBI/other rank and file IC employees who will have been questioned and will be asked to turn over any pertinent documents. Especially the FBI guys who are higher ups who were close to Comey/McCabe.
*Media outlets and social media organizations*
-Facebook, was confirmed hacked by Russians (Zuckerberg testified in front of Congress about this, wasn't really helpful)
-Twitter, huge bot activity, suspended a number of accounts related to Russian hacking (most importantly Guccifer 2.0 who confirmed worked with Roger Stone)
-Reddit, huge bot activity
-Fox News and higher ups associated with Fox, funded by the Koch brothers who are super wealthy conservatives who are likely in deep with GOP financially
-Breitbart, far right news outlet formerly headed by Steve Bannon
*Political/other organizations*
-DNC, was confirmed hacked during the 2016 election
-GOP, specifically financial records related to campaign spending, where is the money coming from
-Blackwater, independent military contracting company founded by Erik Prince. Prince is related to Betsy DeVos and is alleged to have masterminded the meeting in Seychilles between Kushner, Flynn, and Sergey Kislyak.
-NRA for financial ties with Russia and the GOP, potentially other politicians unrelated to GOP
-Cambridge Analytica, data mining firm founded by Steve Bannon, thought to be connected to the hacking of Facebook by Russia which allowed Russia to spread mass disinformation
*Russians and miscellaneous people*
-Vladimir Putin, Russian President who has met with Trump several times in total secrecy. Has presumably killed political opponents and helped orchestrate the Russian meddling in the 2016 election. Tbh it's a pipe dream but if Mueller can actually get Putin with evidence of actual crimes it could set up a huge breaking point between Russia and pretty much the rest of the world. Could catch a lot worse than sanctions.
-Sergey Kislyak, Russian ambassador to the United States who has met with members of the Trump campaign in private
-Christopher Steele, British spy and author of the famous Dossier that provides more details on Trump's activities in Russia
-Stormy Daniels, pornstar who confirmed fukked Trump and was paid hush money under threat. Was recently arrested and could potentially lead back to Trump
-Michael Avenatti, attorney of Stormy Daniels who has claimed to have damaging info on Trump and Cohen
-Igor Sechin, head of Russian oil company Rosneft. Currently bogged down by economic sanctions, a popular theory postulates that a deal is in place to give Trump a huge amount of Rosneft money that would be made after the economic sanctions are lifted.
There's more but shyt man