To install the Curt Class II # C12280 hitch on a 2005 Chevy Malibu Maxx, you would need to drill two holes, one in the underside of each frame rail, as outlined in the instructions I've linked you to.
If you'll be doing some light duty towing with your hitch, you might also need the following:
Trailer wiring harness, part # C56013
Ball mount, part # C45520
1-7/8 hitch ball, part # C40001
2 inch hitch ball, part # C40018
Locking hitch pin, part # e98882 view full answer...