The modes with pictures are automatic modes created by the camera for a specific purpose, which although can be fun to use, you have no control over how the camera works so we won't go into them here.
The four modes I recommend you use are as follows:
P - Programmed Automatic
I know what you're thinking, I said dump the auto, well this mode is a little different, this mode is automatic, there are several programmed shutter speed/aperture combinations that you can select between, so whilst you're learning I recommend this mode, that way you can cycle through the programs using the control wheel on the back/top of your camera to select the settings you wish. Oh, and if the light gets low, the camera won't pop the flash up every two minutes!
A - Aperture Priority
This mode allows you to select the aperture you wish to shoot at, again using the control wheel, the camera will then select the appropriate shutter speed for you.
S - Shutter Priority
This mode allows you to select the shutter speed you wish to shoot at, again using the control wheel, the camera will then select the appropriate aperture for you.
M - Manual
This mode allows you to select both the shutter speed and the aperture that you wish to use, the camera will not adjust either of these settings for you.
I only recommend this mode if you understand exposure.