Paramecium move by moving their cilia, which are hair like structures that cover the outside, or pellicle, of the organism. The cilia also aid in eating as well. You can find more information here: http://101science.com/paramecium.htm
1 Additional Answer
Paramecium move in 2 different directions, forwards and backwards. They contain hair like spikes called cilia which they use to move. They also tend to spin while moving.