You pay the fee, you get into the anthology. Before entering one of these contests, make sure that the prize includes publication in a periodical that has a history, a reputation or a significant circulation. A writer recently called me to ask about a letter he'd received congratulating him for having registered the copyright for his book and offering to represent his book to major publishers. He was smart to be suspicious. In years past, many writers were taken in by a literary agency that sent out brochures to Writer's Digest subscribers.
Any generic solicitation is likely to lead to a request for money.
You should still perform due diligence, but this could represent your lucky break rather than the come-on for a scam. Good literary agents receive all the submissions they can handle through listings in directories and word of mouth. Only marginal agents go out on the hunt in these ways. One agency that indiscriminately spammed Internet newsgroups in a search for clients and then waged a campaign of harassment against writers who tried to expose it actually exposed itself when it asked prospective clients to submit three poems, three short stories, three articles or three book chapters. If you're online, it's easy to get fast feedback on questionable literary outfits.