I'm not sure weither you are asking where you can get a avatar of your toon or how to make one yourself.
You can either ask someone to make one for you, some ask for ec, some offer drawings for free, there is also DeviantArt - you can commision alot of the artists you can find there to make a drawing for you, they usually ask for real money.
If you are asking how to make one yourself:
Most people use sai or photoshop to draw but there are other programs like manga studio for example.
You can get a 30 day free trial of sai and then just get yourself a cracked version if you like it.
Having grafic tablet helps alot! Drawing with your mouse is a pain.
If you are looking for drawing tutorials, just use google, there are millions of different kinds, for just about anything you can imagine. Or check youtube.
In general:
Keep flipping your drawing - it makes it easier to see if something is wrong.
Don't be afraid of colours and contrasts
Take breaks, sometimes stopping for a while and looking at something else makes it much easier to see where your drawing still needs tweaking once you tab back to it.