I recently got my first comic series accepted after YEARS of rejection. I'm currently published with an independent publisher called Insane Comics and I'm friends with several published authors who have given me tons of advice along the way so if you'd like I can pass what they told me onto you.
1. Start from the top! I know a lot of people think they wanna start with the smaller publishers then go up, which is actually the opposite of what you want. You may never know, one of the big wigs may be interested in your story so it doesn't hurt to start from the top and work your way down. Also don't be afraid to pitch to literary/comic agents since they can help push your story to publishers and producers.
2. Be Prepared for Rejection.Very rarely do stories get accepted on the first try. Some of the greatest authors and creators have been through numerous rejections. It comes with the territory. Whatever you do, don't get offended and don't take it out on the publisher who may have rejected you. The comic industry is very small and you don't want to burn any bridges. Simply get up and try, try, try again. The worst they can say is "no."
3. Remain Professional. Do this everywhere! Be professional in your inquiry with no typos, providing all the requirements, and little to no grammar mistakes. The inquiry is where they get their first impression of you and first impressions do count! The more courteous and professional you are, the more likely they're going to take a further look into the pages you supplied. If in the first sentence there's a bunch of typos, they're going to scrap your e-mail. It's the nature of the beast, they're looking for a story that can make them money on a professional level so their expectations are high. Also, most likely you'll also be advertising online a bunch and remain professional online as well, since publishers will most likely look at this too. Some don't but some do so it's best to be safe. If you have a crummy internet identity and reputation this will also hurt your chances too. Think of it like a job interview, and some jobs do look up your internet background to see if you're professional enough to represent their name.
4. Do RESEARCH! I cannot stress this enough. Research the publisher. Make sure they produce stuff similar to your comic. See if they're even open for submissions and if they accept unsolicited submissions/manuscripts. If they have a particular person who handles comic submissions submit to only that person!! If you submit to the wrong person who doesn't handle comic submissions, you have just struck out and you won't be able to submit to them again unless you have a different comic to send. Familiarize yourself with their company <--THIS IS A HUGE BONUS! Read their "About Page" their news updates, everything. Learn all you can as you can put this into some inquiries. Some will require you to know about their company and will want you to know them on some personal level (some don't) and when you've learned what they're doing with their company, that shows you took time out of your day to care about them. (Note: If you're not sure who to submit to, you can e-mail and ask them. This not only helps you perfect your initial submission but also establishes some connections between you and them).
5. Polish your Inquiry. The inquiry is where they get their first impression of you and your story. You want this to be short, sweet, to the point. You don't want this to be two pages (unless it says differently on their Submission Guidelines, which is why you definitely want to have that section practically memorized). If you're unsure of how to prepare an inquiry I highly suggest checking out Query Shark. They mainly handle novel-related manuscripts but inquiries are needed for everything: comics, screenplays, etc...so expanding your knowledge on this helps out a lot.
6. NEVER talk about pay! Some publishers have it displayed out in the open how much their creators get in royalties, but most don't. If they don't this is perfectly okay! You DO NOT want to talk about pay until they send you the contract. Do not ask them how much creators get in royalties in the first e-mail. This is a big no-no. When you get that contract you can go from there about pay and royalties but until then, don't mention it at all until they do.
7. Requirements All publisher have requirements and these vary from company to company. You want to memorize their Submission Guidelines like the back of your hand. Provide EVERYTHING they require and make sure you're following it to a "T". If they don't want comic pages in attachments but in the body of the e-mail, then make damn sure you're not sending it to them as an attachment; they will scrap your e-mail then. You want to get their attention as much as possible. Check several times before you send off that initial e-mail you have everything in correct, proper, professional order.
As a final note, you don't really wanna share your comic on the internet if you plan to send it to publishers. They're looking for original stories that, for all they know, have only been seen by your eyes only. Why is this? Art theft is a huge reason and they like to be the ones to have seen your comic other than you.
Like everyone else has said, you could always self-publish but it is pricey. As someone who is with a publisher there are plenty of perks and opens up a lot of doors and it really does help you on advertising. As long as you do your research and remain professional, you're halfway there.