Before you consider publishing, you'll absolutely want at least three or four people to read it through. Preferably people knowledgeable in the subject and genre. Then you'll want to edit it, get people to read it again (the same people if they can stomach it! though others would be fine too) and repeat until you're very happy with it.
Then it's up to you. If you aren't fussed about the money, opportunities and prestige (none of which are guaranteed by any means, I should say) that comes with publishing through a publisher, then you can avoid the hassle and just self-publish via Amazon etc. Else you'll want to send it out to as many publishers as possible. You'll have a lot of no replies, a lot of blunt rejections. But - unless you do get published, which is unlikely on your first attempt but possible - the most helpful will be the one or two publishers who give you some robust, honest feedback alongside their rejection.