Is it clustered SQL Server or Stand alone SQL Server?
If it is Stand alone SQL Server, Installing Service Pack is pretty straight forward:
1.Down load and Read the read me file of the Service pack you want to install.
2.Backup all the databases, script the logins, jobs and save them in a safe location.
3.Do not stop any SQL services.Service pack installation will take care of that.
4.Start and follow the service pack install wizard steps.
5.At the end it will ask for a reboot. Because we did not stop any services at the start of the Installation.
Note: Before applying Service pack to a production server, Test it in a Test server, document the steps and apply for the development and QA servers and then finally apply for the production box