I'd start by doing some research. Nowadays publishers big and small operate in the internet, offering hard copy scores as well as digital downloads. Some googling should give you quite a lot of publishing companies. Some of them can even call periodically for scores, or at the very least admit submissions for consideration (or say flat out that they don't accept submissions). I would discard the big companies and concentrate on the smaller, independent publishers. You will have more chances there. Look at their catalogues to have a feel of the style and quality of music they publish. Some of them will specialize in certain niches, such as pop, or music for school bands, or for clarinet choir, or deal with original music or with arrangements. You get the idea; if a publisher looks for educational flute duets for beginners, don't send them a symphony. If they are into avant garde, don't send them a classic menuet.
I expect publishers do not except a perfectly notated score (they would have someone to edit the score and make it look professional), but try to notate your scores as clean and detailed as possible. Also, a live recording is almost a must, because it demonstrates the actual viability of the music. If you can't provide a live recording, try at least to make a high quality audio mock up.
Then it is a matter of perseverance. Once you get you first piece published, if it sells well, there is a chance that the publisher will ask you for more. To sum up, find your niche and work your a55 off.