Getting Started
The first thing you’ll probably want to do is choose a theme. There are quite a few of them to choose from. Just go to Design/Themes and browse through the available themes. Click on the one you want to try out. I usually have 2 browser tabs/windows open, one showing the admin panel, and one showing the frontend of the site I’m working on. View the frontend of your site (found at your-username.wordpress.com) to see if you like the theme you’ve chosen. If not, go back and choose another theme until you find one you like.
Creating Categories
The next thing to do is create some categories for your posts. To do this, go to Manage/Categories and click add new. Now when you write a new post you will be able to select one or more of the categories you’ve created.
That’s the gist of getting your site up at WordPress.com. There are some great resources to be found at WordPress.com Forums if you need some assistance with any aspect of managing your site.