There has been an automatic upgrade plugin for WordPress for quite some time now. And since WordPress version 2.7 the automatic upgrade feature has been part of the WordPress core. But there are some hosting accounts that restrict the automatic upgrade feature from working.
With any WordPress upgrade, I highly recommend backing up at least your wp-content folder and database first. Then when you see the nag to upgrade WordPress in the dashboard just click the link to automatically upgrade. In the next screen, you might be asked for the hostname, username and password. That is simply the FTP information used to upload files to your site. The FTP information should have been or can be provided to you by your hosting account.
Here is a link to the WordPress Core Update Host Compatibility checklist. You can see if your hosting account passes the test. It also has some information to fix or bypass a few of the more stubborn hosting accounts.
