In order for 'uncategorized' not to show, you have to first of all create and then check another category or categories, and then you have to uncheck 'uncategorized'. And actually there is a way to set one main category to show as a default rather than 'uncategorized' and that is to go to the dashboard for your blog, scroll down the page til you see in the left-hand side panel 'Settings'. From the 'Settings' menu, choose 'Writing'. On the page that comes up you'll see an option called 'Default Post Category' and you can choose from the Categories you've already made so that 'uncategorized' won't show up.
If your blog doesn't have a main category, you could always create one that's a bit more generalised than most just to stop it defaulting to 'uncategorised'. For instance, I did this in my art blog and just created a category with the name of the blog itself. So instead of it saying 'posted by Val in Uncategorized' it says 'Posted by Val in Art by Val Erde' (I won't give the link in case it looks like I'm spamming!)
I hope that helps, I remember when I was new to WordPress, it took a while to learn it.