Euglena, amoeba, and paramecium are all unicellular eukaryotes belonging to the Protista kingdom. Unicellular protists have a nucleus and membrane-bound organelles so even though small, they are functionally complex. There are about 30,000 known species of protists and they are commonly classified according to their patterns of movement.
Euglena moves with a flagellum and is classified as a flagellate. The flagellum allows the euglena to propel through the water quickly with whip-like motions.
Paramecium moves with cilia and is classified as a ciliate. The cilia, microscopic hair-like structures, act almost like oars in the water, allowing the paramecium to rotate, and angle forward and backwards.
Amoeba moves with a pseudopod and is classified as a sarcodine. The pseudopod is like a "false foot" or extrusion of part of the cell.