Can I put turbo or supercharge a 03 Buick Regal

Why? Do you have many thousands of dollars for parts, labor and dyno tuning just laying around to sink into a 2003 Buick? It could be done, but would be very expensive.

If you like the car, look for a Regal GS which will already have the supercharger. The engine is built from the bottom up to be stronger and the transmission is also more robust. Then you can make some simple tweeks, like changing the blower pulley and taking the kink out of the exhaust. With a good strong stock supercharged 3800 you will be surprised at the performance.