The trans cooler will look something like this:
Probably painted black, and to the rear of the engine. The water lines will be attached to the ends of the cooler, probably 1 1/2 -1 3/4" lines, the transmission fluid lines go to the two smaller fittings, probably 1/2- 3/4" hose. Remove the two water hoses, look down the middle of the cooler for any debris. You should be able to see through all the little cooling passages to the other end.