Some times you iPod gets dirty because of the protector or case you are using.
For example this one.
Look the little stains in the case, this dots get the back of your iPod dirty and is pretty difficult to clean your device with a simple cloth.
You will need a cloth and ...
Just have less as you can of hand soap.
The little the better.
In the index finger you take a drop of water.
Mix it between your fingers.
Clean your fingers in the cloth.
Take the cloth and circle it over the dirt on the back with the wet tip of the cloth, after that pass the cloth over the back to remove wetness.
Look the dirt in the cloth.
That's it! Your iPod Touch is clean.