you cant make a "perfect" painting ever and you can't make a "near perfect" painting unless you are a great artist. there is no true method, just study the art of other artists and try to learn from it
Some tips are in order?
1) Make it big. Being able to identify what it is would be nice.
2) Avoid details. We can't see 'em when the picture is so small!
3) Avoid whitespace. It's boring; try to fill the canvas with something other than blankness.
There are surely a million other tips, but those are the most important in my eyes.
You should...
-Draw what you think best represents you -If you're not a great artist, draw something simple that you can handle.
-Try you're best.
-Try printing out a picture or viewing what it looks like before or while you draw of what you have in mind. This may help you get a better idea of what you are going to draw for your avatar.