You should probably follow the Cisco documents first very closely. Depending on your version, etc things are different.

first things:

BACKUP!

Pull a drive on the Publisher or any server you upgrade if you can. Quick and easy rollback if it fails.

For a cluster, it's always Publisher first, reboot, then Subscriber, reboot, then next Subscriber, reboot, repeat.

Many things go on though in the background depending on what kind of update you are doing. So read the "readme" file carefully.

cheers and good luck