A snail moves with the help of:
Foot
A thick, muscular foot is present at the base of a snail's body. Foot slides over the ground due to alternate contraction and relaxation of muscles, like a wave. Snail, while moving, leaves a mucus like substance on the ground. This is secreted to make the surface smooth to move.
The image above shows a snail in upside down position and the foot can be seen distinctly.