You can create an "about" page (there is a default about page, and you can use that, replacing WordPress's content with your own) and then set that as a static front page. Here are directions: http://en.support.wordpress.com/using-wordpress-to-create-a-website/
It is probably best if you are using your wordpress.com site as a regular blog not to have a static front page. Repeat visitors will get tired of clicking past your "about" page in order to get to your fresh content.
Instead, consider creating your about page and making it a menu item that people can access easily. You could also create a text widget with some small blurb about yourself and then link to the about page for further information.
Here are more useful links for you: