Transverse: In a transverse wave the particles don't move along with the wave, they move up and down as the wave passes by.
Longitudinal: Unlike the Transverse wave, the particles oscillate along the same path as the wave. As one particle collides with the next particle it transfers its energy sending it to the following particles.
Surface Wave: In a surface wave the particles oscillate up and down, as well and side to side. Moving like this gives them a circular motion.