How the Russians did it in 2016, to answer OP's question, was a highly sophisticated, multi-pronged effort that included everything from machine hacking (the simplest, in all actuality) to molding public perception through disinformation, lies, confirmation bias, and funding of domestic groups to facilitate same. The US was in the perfect position for Putin to impact the outcome of 2016: his hatred of Hillary was only equaled by the rightwing cabal that has been out to destroy all things Clinton since Bubba beat Poppy with an assist from Perot in 1992; as SoS, Hillary focused on Putin and Russia's elections with laser-like accuracy (remember, she was [italic]very[/italic] vocal about Putin's manipulation of Russia's elections; it makes sense that Putin interfered in her's); and, Putin built Trump to position him as an asset, so when Trump announced he was running, it was manna from Heaven.
Putin and his oligarchs funded so much of what Republicans did throughout 2016 that it was obvious what was going on. The NRA alone was a large enough cash pipeline. Paul Ryan and Mitch McConnell were caught on tape discussing how to hide Russian money in political campaigns, and the NRA provided the means. There is substantial evidence that the NRA was complicit, knowing full well that what they were doing was dangerous and if caught would mean the end of their organization. And now, we have the chance to see that through via NY's suit against the NRA. Let's hope that they aren't able to slither to Texas and reform under a new organization, bankrupting the existing NY structure and leaving them unaccountable.
Then there's the troll farms, Russian media, and Facebook's complicity with those efforts. If nothing else about 2020 was made clear, it should be that social media has far, far too much power. Democrats enjoyed it when Twitter, fb, Google, and Amazon finally banned Trump (which, to be clear, was not done out of the goodness of their hearts, but more due to their bottom-line financial worries) and now that the world is aware that anyone's voice can be silenced, the Republicans and far right will use it as a weapon if no guardrails are installed.
And let's not forget that it was the Russians who hacked the DNC servers and turned over the data to Wikileaks to publish, which in turn, put Hillary's emails on the front page of the NYT every day for months on end, and gave Comey cover for stepping into the election 10 days out.
In the end, the 2016 election was the perfect storm. Everything came together for Putin to achieve his goal: Hillary is never going to be in the position again to have any power, and specifically, power over Putin. After spending 50 years harping on Russia, it laid bare the real Republican agenda which is, of course, power at any cost, when Republicans flipped their position and suddenly Russia was no longer the threat that Mitt Romney pointed out in 2012. There were simply too many people around Trump that have been shown to have ties to or affiliations with Russia to not seriously consider the events of 2016 with an eye toward proving Russian interference. For example, Russia wanted Manafort to be involved with the campaign, and within a matter of weeks of him being named head of the campaign, the sanctions and language regarding Russia were removed from the Republican platform. And, of course, the Republicans had no platform at all in 2020.