The first step is creating a profile on a social network site. This would be the central of your persona on the Internet. From there you can branch in many directions: online games, youtube videos, other websites that work based on their community, forums... The key here is to be consistent and always go back to your central profile.
Finally, if you really want your mark on the Internet you may consider getting a personal blog. Wordpress and Blogger offer free blogs which are suited for most people. But for those who really want the virtual equivalent of piece of land owning a domain name is the ultimate goal.