Does your Regal have a Console now or is it a column Shift? I assume you must have bucket seats so you will have room for the console. I am going to assume that you don't have a console or floor shifter currently.
My experience with Center Consoles is with my 70 Camaro so bear with me because the G-Body may be a little different.
1) figure out how to get the plastic shift handle off. They are generally held on with some kind of snap ring or wire clip. It may pop apart allowing access to the snap ring or there may be a slot where you can push out the clip. Maybe someone else on the forum will have more information to add.
2) Genearally the Console is probably screwed to a couple of brackets that mount to the trans tunnel and probably to the bottom of the dash as well. Just start removing things and looking for screws underneath. I would look under the Ashtray and in the bottom of the armrest/storagecompartment. On my Camaro once you unscrew 2 screws in the bottom of the storage compartment, the whole storage compartment lifts out exposing some more screws that fasten the console to the floor brackets.
3) Once you get the console out, before you go through anymore work, I would test fit it to ensure it will fit under your Regal's dash. In the Picture, the console looks tall. You may need to remove your Regals Ash Tray if it is the type that mounts under the Radio. It is just held in with a few screws.
4) There will probably be some brackets that are spot welded to the trans tunnel. Get a spot weld removing bit, or any drill bit big enough to drill out the welds so you can put the brackets in your car. Take some measurements so you know where they go.
5) The shifter is probably held to the floor with 4 screws plus a couple of more around the boot where the cable passes throught the trans tunnel. take measurments of where the shifter mounts and where the cable passes through the floor.
6) Go under the car and disconnect the cable from the trans. Take any brackets go with it. I think there is one that bolts to the trans pan and you will also want the one that the end of the shift cable connects to. I believe that the brackets that connect to the Trans are different when you have a floor shifter so grab everthing.
7) FYI, the cars with Floor shifter still have a linkage running up to the column, This drives your gear indicator and I think your reverse lights.
8) Maker sure if your car is a 3spd that this donor car is a 3spd as well. Things get kind of sloppy if you mix a 3 speed shifter with a 4 speed trans or visa versa. It will work but the gear indicator will be off and you may not be able to get it in all gears.
9) If the Grand Prix is being scrapped, you should remove the inner seat mount brackets from the floor while you are removing the console brackets. If you don't need them, you can probably find someone else on the forum that wants to convert to buckets.