The very first question that you need to ask yourself when wanting to make a living from drawing or painting is 'How much do I want this?' Because you need to want it A LOT to make it succeed. It is very hard work, but very rewarding too.
In very many cases, artists become multifunctional people and few make their entire living from drawing or painting. In my case, I work full time but use all my off time to work on and promote my art. I also teach drawing and painting. I find that many artists go this route to bring in additional dollars.
Also, you need to find what you do best in art and keep honing that skill. Become known for it, promote it, market it. No one will come to you. You have to work VERY hard to sell your art and be prepared to get a lot of rejections. Artists need thick skins because there are a lot of critics in the world.
To even approach a gallery you will need a minimum of 10 - 20 recent paintings or drawings and then galleries will take anywhere from 30 to 50% in commission fees. Often its better to market your work outside a gallery setting initially.
If you draw, say cartoons, then target organizations that buy them. Magazines, periodicals, newspapers, book publishers etc. Buy a current copy of the
Artists & Graphic Designers Market to access contact information and try some submissions. You need to meet deadlines, be creative, be prepared meet editors requirements to a 't'.
In a nutshell:
Practice constantly (and that means daily no matter what) and be the best that you can in a specific genre or medium. Know it inside out so you do almost do it in your sleep.
Be prepared to work very hard at marketing and promoting your art. Yes, you'd rather be drawing, but if you want to make a living from your art, the marketing side of it is very large and very time consuming. The production of art becomes the icing on the cake.
Look at other art related areas that you can make money from. Once your skills are good, can you teach others these skills?
Start out pricing your work comparable to other artists in your area who do similar work. Do some research. How long have they been around, what is the medium, are they technically sound, does their work sell well? Who is buying it?
Review the economy in the area and target those who still have dollars to spend on art. They are there, you just need to find out who they are and where they are? For instance, horse owners, boat owners seem to have surplus dollars to spend on luxury items so target them if that's your strength.
Be serious about it. Treat it as a business. Make a business plan, have goals and aim for them. Dedicate resources to marketing and look professional. Produce a body of work. Hold a local exhibition if you can't get into a gallery.
Its not easy to become known and respected in the art world, but it can be done. Only then will the dollars follow. You have to be dedicated to make it work. You have to want this more than anything else in the world. Remember, no one will come looking for you out of the blue. You have to make them come to you.