Are there any reliable websites that do minifigure trading? I had a look around but couldn’t find much at all.
There is a site for explicitly this purpose, called aptly swapfig.com.
It works by connecting other users either via a wanted or an offered ad, and if the other party accepts the trade you have to exchange postal info and send the minifigure. When the minifigure is received you have to check a box in the trade process page and you can leave a comment. Same if the item is never received. Like Bricklink, building a good reputation is necessary if you want to be trusted in making exchanges.
Or if by trading, you mean buying and selling, then there are many suitable websites:
Here you can sell any minifigures you have and use the revenue to buy others, all the while enjoying the benefits (buyer and seller protection, market share, infrastructure) of an established site. Using these sites might not be straightforward for the first time, so be sure to read up on their own rules and customs, or ask around to learn what you must/should/could (not) do on them.
If, however, you mean "trading" rather as swapping, without involving money, be mindful that there can be huge differences in the value of a minifigure. Depending on age, condition, accessories, rarity and of course desirability, there can be a price range from under a dollar to hundreds of dollars for a single minifigure.