Here is the quick and dirty version. If you look around the forums, you should find lots of information on this topic. First thing you always do is back up the file system and the database in case you need to roll back. Double check to make sure you have the web.config file backed up as you will need it after the upgrade. If you can, perform the upgrade on the copied production version (diferent files and db than what is running) and then switch the home directory in IIS. This has the least amount of downtime for the production site.

We always use the Install packages to upgrade. Download the 4.7.0 version, overwrite the files on the existing site. Open the new web.config and updating the connection strings and machine keys along with any other customizations from your original web.config. Navigate to the site and you are it should upgrade.