It's pretty easy to cheat online using engines. Hans actually admitted he cheated a few times online when he was younger. Chess.com claims they have strong evidence he cheated more than he admitted but who knows.
Over the board, there's no evidence Hans cheated against Magnus or anyone else. He beat Magnus and Magnus threw a bit of a hissy fit and withdrew while implying Hans must have cheated. Hans was actually having trouble discussing his thoughts and different lines after some games which didn't really help things but still there's no actual evidence.
As for how you actually cheat over the board; spectators can signal, small earpieces, other communication devices etc. The anal beads thing was an absurd example of something that is actually possible.
At the end of the day, Hans is now in the top 20 in the world after fighting the accusations. It's actually pretty impressive considering he was effectively blacklisted from getting invitations to tournaments. At this point, I'm rooting for him because he's somehow far less insufferable than most of the people that accused him of cheating.