I'm not a professional surveyor, so I don't have a moisture meter. The first thing I do is to look for any structural damage such as dings that go deeper than the gel coat. Then I look for screws in the transom such as transducer mounts. I take out the screws and look to see if any water runs out. Replace the screws using 5200 to keep them waterproof. Finally, I take a ball hammer and tap the outside of the transom fairly firmly about every 4" interval. I listen for any change in the sound. A wet spot in the transom usually goes from a sharp tap to a more of a dull thud. A really bad spot sounds hollow.
You can borrow or rent a moisture meter, but in my experience, it's often hard to interpret the results. The calibration is not absolute, so the best you can do is to look for large differences in moisture content in different regions of the transom.
I will also stand on the anti-ventilation plate of the outboard motors and try to jump up and down looking for any flex in the transom.