What is the context in which you are trying to explain these things? Are you in person? If you are in person, getting yourself a slinky could work well enough (slinky swung back and forth = transverse, slinky compressed and expanded along a line = longitudinal). When it isn't possible to communicate with images or graphics, look for ways to show meaning with tactile elements or descriptive explanations.

A police siren has alternating highs and lows, with a smooth progression between them, spaced at regular intervals. That's a wave function accessible to the blind.

Temperature over days or the position of the hour hand on a clock, the distance between the ground and a point on a rolling bicycle tire are also wave functions.

Longitudinal waves move in the same direction as the flow but transverse waves move perpendicular to it. Traffic at a stop signs could be considered a longitudinal wave. The car in front slows down and stops, causing the car behind it to slow down and stop, which causes the one behind it to slow down and stop, etc. Then the car in front speeds up, and the car behind it does, too, etc. It's longitudinal because none of the cars changed directions, they all just changed speed.

A transverse wave moves perpendicular instead of parallel. If you're in the swimming pool and a fat kid jumps off the diving board he creates a transverse wave. Water moves away from him but it moves upwards as it moves outward, forming a wave above the surface of the water. It's transverse because the outward expansion of the water is revealed by a 90 degree, perpendicular upward push of the water that we commonly call a wave. A few seconds after he jumps in to the pool the wave will reach you, and if you were only in knee deep water you'll feel the wave rise halfway up your thighs.

Woo, Thanks guys, I think these examples will help me in explaining these waves. Just for the context, I was trying to explain them in the context of earth quakes.