Vanity publishing is a kind of publishing every serious author should avoid at all costs. How do you know if you're dealing with a vanity publisher?
It's very simple. A real publisher will never ask you to pay them for the privilege of being published. Why not? Because publishers, real publishers, will not accept your work for publication unless they are convinced that they will make money from it. There is no reason to ask you to pay them, because they will make money on the merits of a well-constructed piece of writing.
Vanity publishers, on the other hand, will ask you to pay them an up-front fee for the publication. They don't care if your work is of good quality, because they don't care if it sells. Why don't they care? Because you are paying the up-front costs, plus a tidy profit for them. If your book never sells, it's no matter to them. In fact, considering that they don't bother looking at the quality of your writing, they are probably assuming that it won't sell--except to friends and relatives who feel obligated to purchase your book out of a sense of loyalty.
Do not let a publisher talk you into paying them for the privilege of publishing your book. If the book is of high enough quality that people will want to buy and read it, it is their privilege to publish. And if it is not of sufficient quality to interest a publisher . . . doesn't that mean it's pure vanity on your part to think it's worth your hard-earned money to have it published anyway?