Are you talking about self-publishing, or going down the traditional route?
If the former, then try www.lulu.com. It's simply a matter of choosing your options, paying the fees and uploading your manuscript.
If the latter, then you're in for a long and rocky ride. Publishers don't generally want to publish books of short stories, especially by unknown writers. Your best chance is to check out some of the magazines that have stories of the type you write. Most of them will happily let you have their submission (women's magazines are particularly good at this). Otherwise, check out websites for the same thing. Beware the latter though. They don't often pay and once your work is up their on their webzine or whatever, then it's classed as published. Very often, editors and publishers won't want work that's already been published.