Overlaying two nonstatic pictures

I always have been a VB programmer so Java is kind of new to me. But I have to do it for an assignemt of school.

I have created Snake (One of the tenthousand versions) but I want a menu on top of it when you start.

It is an applet and when you run it you should see the basic snake game ran by the computer (that's not the problem). The snake is moving and with the menu ontop you can set the properties of the game, like fieldsize/fieldtype/speed of the snake. The menu is not a problem too because it just excists of 4 lines of text.

Size
Type
Speed
Start game

when you move up or down with the cursor keys a rectangular selection shape will be drawn around the selected text. This rectangle of course moves when you change the selection. So basicly I have two pictures from which the menu is able to redraw but the background (snake game played by computer) is not, because drawing the field costs too much time to do it with refreshrate.

How can I fix this?