WordPress version 2.7 or higher includes an automatic update feature.
Before doing the update, however, it's probably a good idea to make a backup of your database. You can easily do this through MySQL Administrator or, if you prefer, phpMyAdmin.
You should also back up your site files locally. You can quickly do this by downloading the files via your preferred FTP client and then zipping them up for easy storage.
WordPress also recommends that you disable your plugins before doing the update.
To perform the automatic update, log into your WordPress installation as user with administrator access. Then, go to Tools > Upgrade on the side menu.
Then click "Upgrade Automatically."