Facebook users can now create their own avatar.
Simply go to Messenger or the comment box anywhere on the site and click the sticker button. There's no gender option. The customizing starts with the face and skin tone then goes to hair style and accessories.
Right now, the avatars can only be used in comments, chat and Facebook Gaming profiles. It'll eventually expand to posts. To add it to comments, just tap the smiley face icon, then avatar icon.