Start by going through the old timer and writing down the settings. You may be able to simply plug the old timer back in to view the settings when programming the new timer, but don't count on it. I have had the programming deleted when trying to remove old timers. After all, the reason the timer is being replaced is likely because it is faulty.
When removing a sprinkler timer, always take a photo of the wiring to use as a reference, before removing any wires.
Unplug the timer, remove the it from the wall and disconnect the wires.
Most timers will have some kind of screw or push connector holding the wire in place.