Safety is not an easy position as you are sort of the Jacks of all trade for the D. I played safety for a few games (then was returned to the running back) and it can be demanding.
First, make sure that you look around as you should be the last line of defence. So if you notice a receiver in the open and it is not a run play, make sure that you can get to him. Depending on the defence play (zone or man), the safety should be looking for the "deep" threat and stopping it.
Watch the quarterback. Most quarterbacks have a bad habit of zeroing in on who they want to pass to so the direction that he is looking is a great indication.
As for workouts, the safety is usually part of the secondary, so speed is very important. Work on your legs and perform cover drills. Also, work hard on open field tackling. THIS is the bread and butter of a safety. There is nothing worst then hitting a guy and having him break the tackle and run for a TD.