Have you tried reading about it online?
These sources might help:
http://en.wikipedia.org/wiki/Transverse_wave"
http://en.wikipedia.org/wiki/Longitudinal_wave"
As well as the basic understanding that the definition of a propagation of a wave transversely, or otherwise, depends on the direction of motion, accordingly, with the respective element of the phenomenon...
In other words, this is best illustrated by an Electromagnetic wave(such as light), that has a component E travelling, say, logitudinaly, and a B component traveling transversely, or the other way around... The point is, E propagates with the actual motion of the wave(given the polarization factor(typically denoted as k)), and B is perpendicular to that...
As for experiments to determine the polarization, that's very effectively done with a few semiconducting light-filters(essentially plastics), and an incoherent source of light; By adjusting the filters, you can sift through the possible states of polarization of the light created, and obtain either complete translucency or opaqueness based on the adjustment thereof...
I hope I was instrumental somewhat,
Pardon the rambling,
Daniel