Upgrading SQL Server 2012 from SP2 to SP3
1/ Microsoft recommends to test it in your UAT environment before proceeding with deployment in production environment.

2/ Backup system &amp; user databases

3/ If you use analysis services backup Analysis Service configuration files, databases and repositories. Backup files present at location
C:\Program Files\Microsoft SQL Server\MSAS11.\OLAP\Data\
C:\Program Files\Microsoft SQL Server\MSAS11.\OLAP\Config\ directory.

4/ Make sure enough space is available on drive where resource/system databases are present. Resource database is utilized during service pack upgrade. 

5/ Service pack upgrade would require a downtime of application. Make sure application does not access database during service pack upgrade. Make sure you stop all jobs and activities on database before proceeding. you don't need to shutdown database services to apply service pack.

6/ Make sure you are administrator on the system and always run the service pack executable with administrator privileges.

Although instructions for SP2 still relvant for SP3 also, please see the below source. I presume this a standalone instance?

Source: http://social.technet.microsoft.com/wiki/contents/articles/25632.how-to-install-sql-server-2012-sp2-on-standalone-sql-server-instance.aspx