1. On your own (the hard way):
Draw cartoons and send them to magazines. Keep doing this until your cartoons are being published regularly. Be prepared to draw hundreds of cartoons. You will need to buy a lot of magazines that print submitted cartoons, and send each magazine the type of cartoons they're looking for. (For example, a 'Horse' magazine would be looking for cartoons about riding horses ...  a 'Car' magazine would want driving cartoons).
Plan on having a real job in the meantime, however, since magazines don't pay much for individual cartoons. The average magazine will pay you anywhere from $10 to several hundred dollars for each cartoon they purchase, depending on the magazine. It will be easy to sell a few $10 cartoons; much harder to make a sale to a magazine that pays $200!

Your aim is to become well enough known that a large chain of newspapers or magazines will ask you to contribute a regularly scheduled cartoon strip.This is called 'syndication', and once that happens, you have it made!

2. Working for a cartoon company:
You get hired on as an artist (one of many) to help produce cartoons of one form or another. This could be as an animator at Disney, a comic book artist, or as an artist at a childrens' book publisher. There are endless possibilities.
The advantage is that you have a reasonably well-paying, steady career, and your on-the-job experience could come in handy later (see below).
The catch: you won't get this job easily without some accredited training first. Yes, there are college courses for cartoonists!

Regardless of which path you follow (but necessarily if you choose the second one) you will need to get some training in the art of cartooning. You will need to learn to draw better and faster, of course. But an art college can also teach you about the equipment you will need to produce professional cartoons, where to submit your work, and where the good jobs are.

Another advantage of attending an art school is that it will expose you to many different types of artwork, and give you training in the ones that interest you.
For example, Sheridan College (in Ontario) has an Animation course that will not only teach you about drawing, but train you in the field of animation, both traditional and computer-generated.

A final advantage in obtaining a diploma from a college like Sheridan is that it gives you credentials ... and all the work you did there becomes your portfolio. Sheridan College in particular has a world-wide reputation for graduating talented cartoonists and animators ... every year, most of its graduates get jobs in the industry!

You will want to ask your Guidance Counsellor about colleges which offer art, and especially cartooning and/or animation, in Alberta.

Working for a cartoon-producing company will give you good experience. Many cartoonists start off working for a company like Disney for a few years ... then leave and go into business for themselves. You can make a lot of money if you have the talent!