On most DSLR's it depends on the mode (excluding the "Scene" modes"). If you are shooting in aperture priority then you pick the aperture and ISO you want and the camera chooses a shutter speed for a proper exposure at that aperture. If you are shooting in shutter priority you pick the shutter speed and ISO you want and the camera chooses an aperture for a proper exposure at that shutter speed. If you are shooting in manual then you pick the aperture, ISO, and shutter speed based on the light conditions. All DSLR's will also have a bar graph meter in manual mode to show what the camera thinks is a proper exposure.
As to whether that can be done on your camera I think the owner's manual would be the best resource to answer that. According to the images I'm seeing of the H20 there appears to be a manual mode ("M") on the selector dial, however if it's anything like my old H9 changing shutter speed or aperture is a nightmare.