Many people use Adobe Photoshop or Paint Shop Pro to make their avatars. However, since they can be costly, there are free programs available such as GIMP, Picasa, PhotoPlus 6, Gimpshop, and Paint.NET. There may be more but that's all I know of at the moment. Hopefully I helped.
For whatever program you are using, you can search "program name inserted here tutorials" and tutorials should show up. If you use livejournal, you can search the program as an interest and communities that offer tutorials probably. Hopefully one of them helps you with how to use them. I would suggest just playing around if you can't find tutorials or asking a friend for help.
well since youre just starting out... here's a website i made like 6 years ago when avatars werent so high tech!!! so for now, you can start with the basic ways... lol