Jigging is popular for grouper. Jig with soft plastics or hair jigs if you want to use artificials. You can jig with live baits as well.
This is the most common way most anglers will fish for grouper. Find a good spot, get your bait down to the bottom and wait for the bite.
Drifting works well for covering water to find more active fish. Set out your favorite live baits and drift until you find some grouper.
Trolling is not one of the more popular ways to fish for grouper, but it does work. Grouper can be quite aggressive and are known for eating a wide range of baits. They will bite a crankbait or swimbait when trolled right by their face. The key is to find productive water and to get your lures down to the bottom.