The Getting Inside Destroyed Vehicles glitch only works on Halo 3.
Tutorial
To Get Inside Destroyed Vehicles, you will need a Spartan Laser. First, approach a vehicle (preferably a Banshee) and stand next to it (your body must be touching the vehicle). Press RT (Right Trigger), then B to enter/ride/drive on top. Next, charge the Spartan Laser and just as you fire, enter the vehicle. Note that you cannot drive the vehicle.
Another way to get inside a destroyed vehicle is to have someone damage the vehicle with a Fragmentation Grenade or two until it is at the point in which it will blow up if you stick someone with a Plasma Grenade who gets in it. First, get your friend to stand next to a vehicle. Next, have them get in, stick them and board their vehicle. If done right, the vehicle should be damaged or destroyed and you should be able to ride it. But make sure you do this fast, or it WILL NOT work. Two players, an Overshield, and a Missile Pod will work just as well. First have the first player stand next to a vehicle with an Overshield, and have the second player with a Missile Pod fire at the vehicle while the first player gets in. If timed right you will be in the driver's seat.
Note
This has been confirmed to work with the Banshee, Hornet, Brute Chopper and Ghost. You will eventually respawn due to wreckage automatically being removed from the map after a certain amount of time. It should also be noted that many have destroyed a Banshee on the river in Valhalla and that the person inside will float downstream, creating a raft-like experience. Also, this glitch works on all vehicles that you board, force out the driver, and take their place (Brute Chopper, Hornet, Ghost, Banshee), and the Warthog's gunner seat whilst destroyed. The glitch should work on all maps, since maps themselves do not play a part on whether the glitch will work or not; some just happen not to have certain vehicles.