Mafia:III uses the time-honoured mechanics of the cover shooter- walls, crates, and most any other object with a vertical surface can be crouched or leaned against, allowing you to pick a target while remaining out of sight. When the moment is right, emerge from cover to take your shot, then duck right back, either to maintain stealth or to avoid incoming enemy fire.
Mafia:III doesn't change the classic formula much, sometimes even small differences can be important. Those are listed below.
Whistling - Like the thrown stone of many shooters, Lincoln's whistle is used to attract enemies. The catch here is that you can only attract them to you, rather that sending them to the far corner of room, with their backs conveniently turned. The benefit is that, no matter how many enemies are nearby, only one will ever come to check up on a whistle. This means you can pick off even large mobs one by one, so long as you don't raise the alarm. NOTE: While only one enemy will investigate, other enemies may watch him as he does, so don't strike too early. In some areas you may want to try a double whistle- luring your enemy to a corner, then falling back and luring him from there to an even more secluded location. Just be careful- the whistle lures the closest enemy, and you might find yourself with two goons converging on you from different directions, rather than the one you were going for.
Headshots - You always aim for the head in cover shooters, but it's especially important in Mafia:III. An enemy that goes down after a single bullet to the skull might soak up a dozen rounds to his center of mass before falling. Sometimes things are just moving too quickly to line up a shot between the eyes, but if you do have to dabble in a little spray-and-pray, be ready to empty the clip.
Stealth Kills - Most cover shooter's have 'em, but a slight twist in Mafia:III is that even 'boss' type characters can be stealth-killed. Story events generally prevent you from taking out the big bosses this way, but keep in mind that even characters with a high resistance to regular punching can be sucker-punched like anyone else.