Tips from cartoonist Mike Lynch:
First off, talent is cheap. I can walk into any art school and see lots of people better than me. Most of those art students will not succeed. This is because talent has little to do with success. ...
Your talent may help, but persistence is key. If you want to draw single panel magazine gag cartoons, draw 20 every week, throw away the weak ones and mail the rest of them out. Do this every week.
When I started I knew NOBODY. No editors, no other cartoonists. And I didn't know what I was doing. I got addresses from the magazines I looked at in the library and the bookstore. I took the addresses from the masthead of the magazine. It took me 6 months, but I began selling.