Being a cartoonist is a lot like being a novelist. ... You're going to spend more time and effort trying to sell what you've created than you actually spent creating it. There are several different steps that anyone who's trying to pitch their cartoon idea should know before they just go out and start submitting it to anyone who'll care to listen though. Following those steps generally gives you a much better chance of getting your comic serious attention.
Put together some samples of your cartoon in a portfolio. Even if it's just a few strips, it should be enough to catch the buyer's interest and make sure that you have a concrete example of the work.
Search for market lists. Market lists are lists of people interested in the type of creative work that you're selling. By typing in the words "cartoon market list" into a search engine you will seek out those three words in conjunction. You could also save trouble by buying a copy of the "Artists and Graphic Designers Market" that is released every year.
Check the guidelines. Each market list you find will give you lists of people interested in a certain type of product. If you find one that wants cartoons, then check the guidelines to make sure your cartoon is the type the company is looking for.
Submit your cartoon for consideration. Make sure you follow all instructions laid out in the guidelines--what to include, how to send your work (snail mail or email), how many samples must be included and any other important considerations.
Continue submitting your cartoon to different markets until someone agrees to purchase the idea.
Be professional. While your work may be brilliant, it will be a hard sell unless you can present yourself as well as you can the cartoon idea.