It really does feel very much the same as the singleplayer version of the game, except, you know… the hundreds of other people you see everywhere. You'll join the world, create a new character, and start playing. Just make an account when prompted, confirm your email, and then login. It's extremely painless getting it to run.
To try it yourself, you'll need a copy of Mount and Blade 2: Bannerlord installed, and the mod's launcher which you can download here. For now, I'd still recommend trying out the single server in Russia-it fits 800 people, which still seems amazing to me, and there were about 625 players when I tried it. It looks like there are plans to add a server in Europe and one in the US, eventually. But otherwise, Bannerlord Online runs surprisingly smoothly. Most of the lag I experienced took place in menus-checking my inventory and selling items to NPC merchants is a very sluggish process.