How to delete an area inside an image so that it's transparent?

There are a few ways you can do this - it depends on the kind of shape you want to make inside the other. For example, if you are hollowing out a rough or hand drawn type of shape, use the eraser tool (shift+e) _ select the shape to be hollowed,  adjust the brush size, and begin painting. 

If you want to cut out a more refined, detailed shape from within another shape, use the pen or pencil tool — draw the shape you want to remove, and then either:

a) select both your shapes and select Object > Compound path > Make

or

b) select both shapes and using the pathfinder panel (from the window menu) select the "minus front" icon.

You can continue to edit both shapes (use the white direct select tool to isolate one shape from the other) and the effects will update each time.

I hope this helps!!