Hard to say what you're looking for, because it's a bit of a broad topic. I made a quick mock-up that might help you out. It literally does nothing but allow you to jump up and down on a platform, so hopefully you can adapt it in a useful way.
Gravity can be adjusted up and down via the mouse wheel, purely for demonstration purposes. Jumping is "custom" in the sense that you can set a variable to whatever you like, although I made a couple of quick comments in the script on how to achieve something like double-jumping if that's your inclination.
Probably also helps to mention that I set jumping to the spacebar, as is my personal preference.