Standard drawing programs. Photoshop, Paint (If you're going for the basics). If you're a tablet user, you're going to already know which program to use. Some people here do it the old fashioned way with a paper and pencil/paint.
You are allowed to use any program you want @DarthTyrannausarus! Personally, I like to work with Paint, basically because I never took the time to look into other programs. But other options are Gimp, Photoshop, but if you want you can do it the old-fashioned way like @nichodemus said, by drawing on paper, photographing this and uploading it. Whichever way you choose is fine, as long as you made it yourself of course... =)
I just went to the forums to see if there are any open armatar contest. But I wonder, will anyone accept anime armatars? I'm a anime lovar and loves to crop anime images to I get a avatar format out of it and use it on facebook or something.
(You can find the avatar on "http://www.facebook.com/jonbel99"
Users can only be awarded their own custom Armatar if they earned it. Those that have such a custom one did something special for the website to obtain that right...
Another way is to wait for a suitable contest and submit it there. Contests only allow themed submissions though... a new one will be launched soon!!
Like Darkfire said, you need to upload it first in order to use it in a coding line @DarthTyrrannausarus. You can use imgur, photobucket, flickr or even diviantart if you are planning to create a lot. Then use the image code to post ot here! =)