First thing you want to do is turn off the water.
It is tough to see in these pictures. Normally there is a cap on top (the little round area). That can be pried up very carefully with a utility knife. After the cap is off. hold the handle with one hand and remove the screw with the other (using screwdriver)
After the screw is removed, the handle can be removed.
Now, you should be seeing a nut which can be removed with a wrench. Now you will be able to wiggle the stem out of the holding area.
Take the stem to the hardware and they can hook you up with the ones you need.
Yes it is also a good idea to do both.
Hope this was helpful