What you wish to do is certainly very simple to do with an arduino. There is a servo library that has all the software commands needed to control a servo, and reading the status of a switch wired to a arduino digial input pins is very simple. However you should really learn how to write programs starting with the basics, rather then just have someone give you a working sketch just for this one project.
It's a teach a person to fish kind of thing.
Look over the two servo example sketches in the the arduino IDE's File/Example/Servo menu and see if you can make sense of them.