Assuming you know programming basics, it should be quite straightforward to get your servo doing what you want it to do. It's a simple movement, and the examples that are included with the Servo library will definitely get you almost completely there. Start with one of those examples and mix in the button/timing code example and that should be pretty much it.
All commands used in the examples (and elsewhere in the C programming language) can be found well explained online. The first time it may take you an hour or two to fully understand a piece of code, but the next time you see the same command you know what it does and it goes faster and faster. Do experiment! Change values, see what happens, try to understand why it happens, and before you know it you're writing your own sketches.