Twisted pair is not necessarily made up into a crossover cable. Twisted pair refers to the fact that of each of the 8 wires, they're paired up and twisted together, and connected in such a way as to reduce crosstalk and interference.
Each of the 4 pairs of wires may be a 1-1 match at each pin at both ends, or some of the pairs may be crossed. Depends.
Easiest way to check ? Put the ends next to each other, and see if the colours are in the same order. If they are, it's a straight through. If not, it *MAY* be a crossover.
The other way to tell if the two machines are communicating at the physical layer is to see if there is a "link light" on the network card. Plug the lead in, it should go on at both ends. Take it out - you get the picture.
A google search on "Twisted pair" would also reveal the pukka technical details - I'm a software guy who works with networks, I don't plug 'em together very often !