Guide
How a 4-way switch works
A 4-way switch has four screws in two pairs and no common screw. In one position it passes the travelers straight through; in the other it crosses them. The travelers from the first 3-way switch land on one pair, and the travelers to the next switch leave from the other pair.
Finding the pairs
On most 4-way switches the pairs are the two brass screws and the two dark screws. Some brands pair them top and bottom instead, so check the diagram printed on the switch or its box. If the light only works in some combinations, the pairs are mixed up.
More than three locations
Add as many 4-way switches as you need in the middle. The two ends of the run are always 3-way switches.