From Halopedia, the Halo wiki
Halo: Combat Evolved
In the first Halo game, the Banshee model is very different, and the Wingtip Method (described below) does not work. However, with 500% shields (as part of a gametype) or an overshield, a different technique can be attempted.
Starting with the Banshee flipped upside-down like in the other launches, simply PFR under the lower wing in the hole between the two bars that form the wing. If timed correctly, the trick can send the player up to the invisible ceiling in Blood Gulch.
The Wingtip Method is a common trick used to Banshee launch. It works in Halo 2 and in Halo 3.
The basic method is to acquire some weapon that does a high amount of splash damage. From there, a player must find a Banshee and flip it onto its back. The player must stand on top of the wingtip that is touching the ground, and use their explosive weapon on the opposite wingtip. Assuming that the player survives the splash damage inflicted by their weapon, they will be launched to great heights, in Halo 2, this method often allows players to see beyond a map's boundaries.
The method can be performed with a Rocket Launcher or a fuel rod cannon, though the player will need an Overshield if they are not standing on the very tip of the Banshee's wing. Players can also throw a grenade and shoot it out of the air, detonating it prematurely, this trick, however, requires an Overshield. A much safer, but Halo 3 only, method is to simply use a Gravity Hammer, as players are immune to the splash damage dealt by their own Hammer.
In Halo 2, the trick can also be performed using the black shields in the maps Relic and Turf, but an Overshield is required to survive the trick. The host of a game can use a shield to rapidly ascend to the top of Relic's tower. Another way to do this is to make sure you are at the very wingtip, and the Banshee is upside down. Flip it and you should go flying a good distance.
Most of the methods were removed or made more difficult in Halo 3. The trick was likely removed to balance multiplayer gameplay. However, in addition to the Wingtip Method described above (which is still usable with a Gravity Hammer), a new method can be used in Halo 3.
Grab an Overshield, and position a Banshee so that only the tips of the wings are touching the ground. Jump onto one of the Banshees wings until you are on the bigger of the two rods that form the wing, and stick a Plasma Grenade to the tip of the wing you are standing on. If performed properly, you will be launched incredibly high up.
This is similar to a method used in the Halo 3 multiplayer map Sandtrap. If the player manages to flip an Elephant, the screen will say to "Hold RB to flip...wait, what? How did you do that?". If the player stands inside the Elephant while flipping it, he will be launched incredibly high into the air.