you get the batting that is designed for 16 inch spacing. There are two, one for 16 and one for 24. Make sure.
Then I would get a stanly or swingline hand triggered stapler and go for it. This is easy, the insulation has stapling tails on both sides and be careful when installing the top of the run, it will tear with too much weight. Then once in position apply a staple every foot or so, no big deal, your drywall will also hold it in place. Remember, have the vapor barrier on the correct side.