I also had some problems coming from actionscript when I first started. The idea of having persistent visual movieclips doesnt exist in Processing. Basically you clear the stage every frame and redraw everything that you need on the stage every frame as well.
Sounds strange, but thats how flash does it as well - without you noticing

Here is a good table that compares different languages: http://processing.org/reference/compare/index.html

A good way to get to start is to code everything in classes, and every class has its draw function. From the central draw function you call the instances draw functions. This was you can turn on/off what you want to see on the stage easily.