I've put together a few of these things now and they always (for me) start the same way. You first decide you are mad enough, stubborn enough and stupid enough to put one of these things together (I am obviously very stubborn and stupid). That is followed by an idea. A theme or look or something that will set your anthology apart. The selling point, if you will. From there you figure out the format you want (dimensions, page count, story length, etc).
At this point, you should have some idea as to what you are building. So, it then becomes time to start filling your line-up.
Be up front when recruiting people. Chances are your book won't make much money if any at all. What you expect from people and when. If you are putting together creative teams or if they are. What are you allowing into the book and what is unacceptable. Who owns the work and so on. Tell them everything and don't promise anything you cannot deliver on.
Oh, and establish a means of communication on the book early on. Very important.
So, you have an idea of what the book is and what it looks like and who is working on it. Once you get some pages in and hopefully a cover, you then go to the publishers. Use the art and a brief description of what the book is and why you think it will sell and to who. You might go through a few publishers before someone says yes (even Flight got turned down by a few publishers before landing at Image). And if you can't find anyone to back you, be ready to publish it yourself.
So, you know what the book is, what it looks like, who is working on it and how it is getting out into the world. Now you just have to finish the damn thing and get it into people's hands.
I'm simplifying here quite a bit to keep it brief and probably underselling the actual workload, but that should be enough to get you or anyone started.
_________________ Jace Hall Show