They actually aren't.
You gather the work you want and/or put out calls for submissions.
You figure out how much, if anything, you want to pay your contributors. (I always paid my contributors. ) And what rights you're purchasing.
Then you offer them a contract. You basically work up one contract for everybody.
I always purchased the one-time nonexclusive right to publish the work in my book. They owned all other rights.
There are form contracts available online or, if you've pitched the book to a publisher and they want to publish it (which is how my first anthology was published back in 1991) they'll handle that.
They also handle paying your contributors.
Again, if you publish the book yourself, all you have to do is cut checks or use Paypal.
It's actually not that complicated.
But it is time-consuming.
My first anthology sold 20,000 copies and got great reviews and I was hooked.
It's pretty straightforward.