Upload new files as instructed here and run upgrade tool. Upgrade tool is a simple utility that will upgrade your database. It is located in /public/upgrade or just /upgrade if you used .htaccess hack to have clean URL-s. It will require user to log in with administration credentials.
That's pretty much it. Just make sure that all files required for upgrade are properly uploaded and system will do everything else.
If you would like us to have that handled for you, we offer professional installation and upgrade services. Still, upgrade process is pretty straightforward and there should be no problems - upload files, run the upgrade tool, login.
What is the upgrade tool?