If your trusses/joists are 24" or less apart, you can apply drywall directly to the bottom side.
If they are farther apart, you'll need to install metal furring channels perpendicular to your trusses/joists at 16 or 24" centers to fasten the drywall to. You can get away with 1/2 drywall on 16" centers, but 5/8" is required for 24", and I'd use 5/8" anyway just for rigidity and sound barrier. You don't need any special kind, just generic sheetrock you buy from the big box DIY store. 1-5/8" coarse thread drywall screws for attachment to wood, or 1-1/2" fine thread drywall screws for attachment to metal furring channel, every 8" along the field and 2" from the edges.