First of all, finish it. No publisher will consider something uncompleted from a first time writer.
Then put it away in a draw for a few months.
Get it out again, reread it and edit it.
Get as many people as possible to read the manuscript and pass comment. Friends and family aren't a good idea, as they'll not want to upset you if it's rubbish, and they don't generally look for what a publisher's editor looks for. There are various websites around that will give you honest feedback if you reciprocate.
If you're still convinced it's something the public will want to read, get hold of a copy of Writers' and Artists' Year Book and trawl through the listings of publishers and agents who may be interested in what you've written. You then need to send them samples of your work, correctly formatted. Amount and format will vary according to the publisher's/agent's wishes, but it's usually around three or four chapters, typed in a monospace font (eg courier - yeah, I know, it looks rubbish, but it's what they like) and on one side of the (A4) paper.
Be prepared to submit your work to many publishers and editors before you have any success, and be prepared never to have it accepted at all.
Avoid any company that guarantees to publish your book without them even having seen it, or that asks you for an up front fee - they're usually vanity publishers who will take your money and leave you to it. There are one or two reputable 'self-publishing' companies out there, but you should be aware that using them won't make you 'published'.