There is a really cool way this can be done using scripts. There’s also a simpler, more awkward, method that using the built button actions. Unfortunately the scripting isn’t supported by browser and mobile viewers, and the built-in actions aren’t well supported either. The only way you can make this kind of behavior work is if the form is only ever viewed in Acrobat. The free desktop Acrobat Reader is good for the JavaScript solution, and the Mobile Acrobat Reader works for the built-in actions, but it not good for the scripted solution.
If you want a general purpose browser based or mobile solution, then a custom web form is better.