An isolation transformer is the simplest possible arcade part, really. It's a 1:1 transformer, 120v in, 120v out. Sometimes they are marked input and output, but usually it's just two pairs of terminals. Two separate windings. You can easily figure out which pair of terminals makes up a winding with your meter, just check to see which have continuity.
To hook it up, line voltage goes to one winding. No polarity. You will then get the same line voltage (or thereabouts) at the output winding, which you can check on your meter.
All voltages are liable to drift by 10% or more, and an unloaded transformer can read a couple volts higher.
Honestly, they almost never fail. Sometimes they buzz, but it's real, real rare for one to actually go open.
-Ian