From experience at buying a rotted transom.
I would start with a screwdriver or ice pick and a good sized in wrench. Use the screwdriver/ice pick to poke at the lowest point of the interior side of the transom; and any compartment areas below the deck to check the stringers. Also, check any transom areas opposite of any holes on the exterior side say of pitot (speedo) tube, transducers, or ladders. If you find any spongy areas be cautious. Can use the large wrench to hit the stringer/transom with and if you hear a thud I would be cautious. Lastly, if any of the floor is soft you can bet that the springers and maybe the transom are rotted as well. Boats tend to rot from the bottom upwards.
If able the best way is to drill holes in the above mentioned locations and observe the shavings. If their bright yellow your good, if brown or black walk away. Dont drill all the way through but about 3/4 inch or so will be fine. Then backfill holes with 3M 5200 quick set.
You can also pay a marine surveyor...