Can you convert a 99 Mitsubishi Galant automatic to a manual and if so how do you go about this?

It's not the transmition that's hard to exchange, it's reto-fitting a clutch and manual shifter to the car that's built around automatic shifting that's difficult. It should be done by pros if you want to attempt it. (and will probably cost$$$$)

If you're end result is to try and get more power to the wheels, consider installing a 'Level 10' hydromatic shifter and a toque converter re-build. Level 10 claims the torque converter re-build gets 95% of the HP to the wheels and with the hydromatic shifter, gives you faster and more precise shifts. The parts will cost you abour 1200-1300 + installation.