Quote: "We'd have to see your code in order to help you figure out what isn't working."
This might be more of a conceptual problem instead of a coding one. From what I gather, he's asking how to get from say the main menu to the actual game play.
Quote: "but how should I go about loading my other screens, when the correct button is clicked?"
The way I go about this is that I break up my game into 'frames'. The main menu being a frame, the first level being a frame, the options menu being a frame etc. An then I have 3 functions per frame, essentially, a Load, a Play and a Clean Up. The load functions loads in all of the media needed, sets sprite positions and essentially prepares everything for that frame. The play frame is what's repeatedly called inside a loop and handles events such as pushing buttons etc. Finally, when leaving the frame the clean up is called and deletes all media used by that frame so the next frame is free to take over without any worries.
Quote: "I don't want to delete sprites then load new ones, because that would get old fast. Or is that the only way?"
You can just hide your sprites (setSpriteVisible()) however, keep in mind that you're unnecessarily taking up RAM. This might not be your case but imagine if you have over 100 levels and you don't delete anything from going level to level. Just be careful when not deleting the unnecessary media for each 'frame'. It may also mean that AppGameKit has a larger job when it has to clean up all of the media when the app closes.
Happy programming