The Grappling is a very useful tools and one of the series' staple. Here are some tips on how you can use it:
Don't miss out the first upgrade.
After completing the first story mission "Welcome Home", you'll have to immediately start the "Time for an Upgrade" which is practically right in front of you after completing the first mission. This mission will also give you the Wingsuit.
Tethering
The grappling hook's new feature is tethering. You can connect two different objects (or people) then retract the tethered line remotely, causing them to smash to each other. For example, you can use this to smash explosive barrels to vehicles, hook enemies to the walls, and many more.
Vehicle Hijack
You can hijack vehicles by attaching the grappling hook to that vehicle and pulling yourself towards it. You can even hijack airborne vehicles if you managed to grapple them.
Pull yourself towards an enemy
Firing a grappling hook to an enemy will allow you to pull yourself towards them, giving you melee range and allowing you to collect their ammo/grenades without running across the crossfire.
Grappling in mid-air
You can use your grappling hook even when you're in a free-fall or when using a parachute. That said, you can alternately transition between a parachute and grappling hook without hitting the ground.
Breaking your fall
Grappling towards the ground during a fall will allow Rico to slide, making it possible for you to avoid a fatal fall where you can't easily deploy your parachute.
Times you can't use the grappling hook
You can't deploy your grappling hook while underwater or when you're gliding. (Unless you unlock Slingsuit to Reel upgrade in the Traversal Mods) You can however, use the grappling hook when your head is above water or if you break your glide with a parachute.
Hang and Shoot
You can latch yourself at the side of a cliff or wall and shoot enemies from there. This is quite useful in finding a good vantage point to shoot enemies and give you ample space to escape gunfire by grappling or gliding to another position.
Canceling Reel In
Press Circle to cancel reeling in.