You go to TopWebComics.com and over on the left, under the top banner, there should be a link that says "Register." You can click that and make an account on TopWebcomics.
Once you're logged into your account, there should be a link to "Manage Webcomic," and if you click that there's a button for "Register New Comic." This is where you add your comic to their list, and add an image to use as a banner and a description of the comic and all that stuff. You can change this later!
Once you have a comic registered, it'll appear in the list -- though it won't be very high up, since no one's voting for it yet. Go to Manage Webcomic again, and click "edit," and underneath all the comic's information are a bunch of "Vote On Topwebcomics!" buttons -- click on one of those and a window will pop up with some code. If you have your own website, you can copy that code to stick that button on your site, but otherwise, just grab the URL that looks like "http://www.topwebcomics.com/vote/[NUMBERS]" -- that URL goes to the page where people can vote for your comic, so you'll want to share that link with your readers!
(there might be an easier way to get this address but if so I have forgotten it)
You might notice on the Edit page there's also a button for "Incentives" -- basically what this means is that you can upload a picture that people only see if they vote for you. This can be a "thanks for voting!" image, or it can be a sneak peek of a piece of the next page, or it can be something extra, and you can change this out as often as you like. I scribble a really quick, silly bonus comic to use as a vote incentive with every update, since that means people will want to vote to see the extra stuff! You don't have to do this, but it can help you get more votes.
And that's pretty much it! You can vote for yourself, and there's no limit to how many comics you can vote for -- so you can vote for yourself once a day, and you can also vote for other comics once a day -- and the more votes you get, the higher up you are on the list, and the more people will be likely to see your banner when they're browsing the list! I was actually surprised by how many of my current readers found me through seeing one of my comics on TopWebComics.