You can try sending your cartoons to magazines and newspapers.
Send them 6-10 samples of your cartoons with a cover letter and a self addressed stamped envelope so that they can return your work if they don't want it.
There is a 90% rejection rate with cartoons, so don't just send them to anyone. Find newspapers and magazines that have the same audience that you think will like your humor. Also, if you have local magazines and newspapers, they might be easier to get published by as opposed to national papers and magazines.
Once you are published, you will have more credentials and more papers or magazines will be willing to publish you.
You can also make your own self published books and find a store to sell them. The good people at Kinkos or your local copy shop can help you do this.
Good Luck