gary wrote:
My "L"-shaped hallway has a light switch at the end of each leg, a
switch at the intersection of the legs and a ceiling-light the middle
of each leg.

Originally, the ceiling-lights could be turned on/off from each
switch.

I've replaced the original switches with new switches but now only one
switch operates the ceiling-lights.

Should a three-way switch be installed at each end of the hallway and
the four-way switch be installed at the intersection of the legs? If
the answer is "NO", where should the various switches be installed?

How to I determine what wire gets connected to each terminal of each
switch?

It all depends on how the physical wiring was done originally in your
house. There are many possible variations, but they are all
"logically" the same

go here for a diagram that may be of help understanding what you are
up against, and what you need determine about your specific physical
wiring layout.

http://www.thecircuitdetective.com/3....htm#fourbasic