On the three way switch, there are three screws. They should be different colors. Two are the same (usually a brass color), and one is different (usually black). The black screw is known as the common and depending on the position of the switch, the common is making contact with either of the two brass colored screws.

Now the switch has been "flipped" to the down position and the black common screw is now making contact with the other brass screw. Now if you look at the 3 way animation, you will see that by "flipping" either switch, you are routing the current down your traveler wires on an alternating basis.

With a 4-way switch, you have 4 screws (how convienient). These screws are usually colored in pairs, like 2 brass and 2 black. Depending on the position of the switch, the contact is made between the pairs.

Now when the switch is "flipped" the contacts between the screws is switched, and using the same principal as the 3-way, routing the current down the travelers on an alternating basis. Too fun!