First: Market. Who is going to publish this? What length book, presentation, audience, length story, type of story, etc, do they look for? Putting together an anthology on spec and trying to find a publisher for it is 90% likely to never come to fruition. You must target your publisher and pitch them a proposal to publisher something they want to publish, eg, something like they have published before and can make money off of. If it's not something they have published before, you have to explain to them why this is a hot new idea that's going to make them tons of money.
Second: Concept. What is your anthology about? Determining your market will have determined quite a bit of what the concept is. Length, degree of explicitness, orientation, flavor, literariness, etc. Now you refine it. Heterosexual romance? Dominant woman? Gay adventure? A speciality market, like erotic sf or vampire fiction? How many stories, how long?
Third: Terms. Originals only? Easiest to market, hardest to fill with quality material--especially on a limited budget. Reprint? From where? What limitiations? Payment, royalties, author copies, contracts, foreign rights, movie rights... Your agent (you do have an agent, right?) will help you with this stuff. Again, what terms you get for the book and what terms you can offer the writers will depend upon the publisher.
Fourth: Produce guidelines, outlining everything the potential contributors need to know, including place to send paper submissions and paper queries. Good outlines get the right kind of fiction on time with a minimum of paperwork hassle. Distribute the guidelines--this means getting the guidelines to the people you want to have them; generally speaking workshops do not have a wide enough base of skilled enough participation. Your workshop may be different. Send copies of guidelines to your agent.
Fifth: Harvest your crop of mail, crosscheck failed addresses, log your submissions, read and answer your submission as promptly as possible. Juggle submissions for length, style, subject, tone, ect until you have enough words to fullfill your contract while reinforcing and highlighting one another. The sum of the parts should be greater than the whole. Think deeply about the impact your anthology is going to have on the reader, and tailor acceptances and rewrites to enhance that. A synergy develops in a good anthology in which ideas feed off of one another, and writers expand the concept in ways the editor didn't envision. The editor must prune off distracting tangents, no matter how well written, and strengthen the core ideas. Let your agent review the manuscript.
Sixth: Attend your paperwork. Assemble your manuscript. Do your data entry. Collect diskettes and biographies, proofread your manuscript. Lay it out as close to what you envision the publisher producing as possible, using plain typefaces. Suggest cover art & blurb ideas. Solicit quotes from well known authors in the field for use on the cover. Get your agent to solicit quotes >From prominent clients on his list.
Seventh: Fight with the publisher over terms, pull your hair out, soothe insecure authors, double check your paperwork a million times, call your agent and ask advice, turn in the manuscript.
Eight: Bite your nails, keep in touch with the publisher, check your galleys carefully, hound publisher to pay up the promised money. Hound publisher to send the author copies. Get agent to hound publisher. Smile whenever you talk to your publisher and refrain from telling him exactly what you think of the lousy cover. Get agent to tell publisher what he thinks about the lousy cover.
Nine: Redistribute money to authors, carefully accounting for all funds spent. Buy or beg copies of the book to send to reviewers because the publisher didn't bother sending copies to any of the reviewers on the list of reviewers you sent in. Make sure your agent gets a copy of the finished book.
Ten: Buy copies of magazines in which reviews of your book appears, photocopy them and send them to the publisher and authors because the publisher doesn't send you tear sheets. Use highlighters to make sure they notice really great comments by reviewers. Send copies of the reviews to your agent. Use highlighters to make sure he notices really great comments by the reviewers.
Eleven: Hound publisher to cough up royalty statement. Hound publisher to cough up royalties due. Hound publisher to advertise book. Hound publisher to give away promotional copies to appropriate ventues. Hound publisher to sign contract for second anthology. Sixth month later hound publisher for next royalty statement due. Repeat every six months as long as book is in print.
Twelve: Schedule your own readings and autograph signings with as many of the contributors as possible.
Thirteen: Call agent and weep and wail about how much you hate the publisher. Make the agent hound publisher to do what he's supposed to do.
Fourteen: Don't give up your day job.