Similar questions have been asked about 2008, but there appears to be a dearth of information on SQL Server 2012.
- Does it require a reinstall?
- Will it go through an upgrade process (and what does that entail) or is it just a magic SKU switch?
- Is the process exactly the same going from any edition of Trial to any licensed edition?
All you need to do is a SKU Upgrade which is done on the maintenance tab of the installer when you first open it (the first app where you would normally click the "Install a standalone instance..." option.
The process is the same when going from Trial to Standard, BI or Enterprise.
There will be a small outage, so if you are already in production with the server you'll need to schedule a small outage window.