What tools do I need in order to install a tactical stock adapter?
None, but you may want to use a special AR-15 / M16 / M4 stock wrench to snug the castle nut up against the reciever plate, which holds your buffer tube secure. The castle nut does not need to be very tight so a good hand tightening should work fine. A dot of blue loctite will stop the castle nut from coming loose if the issue ever arises.