It's paperwork. You get a visa first (K1 fiancée) that gets you in, saying you're ready to marry. They investigate to make sure it's not a sham marriage and to ensure y'all can support yourselves. Then you go to the US on the visa, and have 3 months to marry him. You send the marriage certificate and file to stay. They investigate again and potentially give you a green card. That needs to be renewed after a few years; or you can file for citizenship.
Many things can lead to a rejection and re-file at any step, but with enough research and preparation you can get through it. I had a coworker marry a nice Ukrainian, go through the process, and they already have two white babies.