Dave you should be able to right away, unless the whole home or condo has extremely elevated humidity, then it's possible you could get false readings.
In those case we would check the walls the following day.
As far as what to look for, darkened areas, bubbles or raised areas in wall paper.
You've got to be a little bit of a detective. What's the most logical path it would follow? Be sure to check common walls, water doesn't stop migrating just because a wall is there.
Ask the homeowner if they mind if you check closets. It's better to do too good a job of inspection, than for them to find missed areas later.
When water come from above, it best to use a Thermal Image Camera, even if you have to rent or or partner with someone that has one. Water from above can run down interior walls and without using a Thermal Camera can be tricky to find.