there are really 2 ways to do that.
1) this is the way it is generally done. you create the transitions from menu A to menu B in a program like after effects and import that transition into the program in between the menus (link menu A to transiton, transition to menu

.
2) this is a hack. you create your menus in photoshop and when you are done designing them, you import them in as slides in a slideshow, put in a transition, render that slideshow by building your project. pull the transition out of your project file and then use that transition in between menus. with 65 transitions to choose from, you can get some pretty nice effects this way.