In-Game you are not able to.
On the forum you may log on and click "Settings", under "Edit profile" you will see "Edit avatar", click on it and you may change your avatar.
Chat with our AI personalities
Go to Menu, then click Avatar. Go from there by downloading a picture.
you cannot do it
First go to your profile with your avatar and select Customize Avatar, it's one of the options on the right. If you don't have Xbox Live then select Profile, then edit profile, then gamer picture.
Transformice happened in 2010.
On the internet. But do not hack, it is not nice when you get banned on Transformice.