The easy part is purchasing and working advertising...You can run Google Adsense and Facebook ads that help a bit. I think DeviantART has an ad service too, and people who use DeviantART strike me as people who like webcomics. Project Wonderful's good too, and if you get handy with that then you can find yourself paying for your own advertising by putting a couple of PW slots on your front page.
Physical advertising is a must. Use meetup.com to find local comic reading and creating groups, but you can also go out and meet people in sketch groups, art groups, 'nerd' and 'geek' groups, etc. who will also likely be interested if you bring a print-out copy of your work and something to hand out that has your URL on it. Is your comic sci-fi or fantasy? Sci fi and fantasy groups are great for that too, you will find readers that way for sure. You can also buy tables at conventions and sell merchandise! Buttons are super cheap and can include an url, so are freebie postcards and business cards, and prints are great to sell if you're just starting out. Handmade zines can be sold at conventions or to local comic book shops.
Free places to stick your link, but require more work to become part of the community:
Reddit.com, where you can dive into /r/comics as well as /r/webcomics, get a nice little piece of flair next to your name to help you promote your comic as you discuss topics that come up in those subreddits.
Somethingawful.com, which has a Creative Convention subforum and a comics-making megathread, where you can both post your comics for critique as well as make a banner that can be permanently featured in the OP if you have enough of an archive to justify it.
Research SEO tricks, too. Sticking appropriate meta tags in your homepage will help Google bring your comic to people, for instance.
Free places to post your comic, but only after using Tapastic
:
InkOutbreak
Tumblr
Twitter
Deviantart.com
Facebook
Penciljack.com
(Just remember to tag your images with a link back because once social medias get a hold of them, it's frequently hard for people to find the source otherwise).
Plus, check around for comics that are similar in style or content to yours. Maybe you can swap guest comics with someone, and trade traffic streams for a day. Fanart for webcomics you admire can also act as a permanent ad for your comic, provided the comic has a permanent fanart archive. Link trading is fun and effective too.
...And finally http://justthefirstframe.com/ is a free promotion service, all you need is an RSS feed for your comic and this awesome person will personally crop the first frame from every page you post, and turn it into an advertisement on their site the day you post it. So, every time you update, you get an ad.
Even with all the effort involved in promotion, the HARD part is making the comic and keeping it going, and where I've had the most struggles. Being a steady presence is where most webcomics fail. D: