From Halopedia, the Halo wiki
Play through the level Uprising until you get to the first outdoor area, then proceed and kill the Brutes. Head through until you get to the large area containing a Wuzum-pattern Spectre full of Brutes. Kill the Brutes without destroying the Spectre (make sure you have one or two Ghosts remaining to use). From the entrance to the Spectre area, drive the Ghost up the wall on the right. A bit of nose-wiggling may be required. Park the Ghost in the small corner and then return by jumping onto a tall rock and slide down to get up the second Ghost (this Ghost is not required but it does help).
Then, drive the Spectre up the wall and over the Ghost, make sure the nose goes up and with a bit more nose wiggling you can get it out and onto the mountain.
From here you can drive right around up Uprising and look down on bits of the The Great Journey. If you wish to return, simply drive the Spectre off the edge and back into the level, however, try not to fall from too high as the fall timer will kill you. You can even proceed to the end of the level and jump down the cliff (and die) and see another Arbiter falling from the sky in the ending cinematic of Uprising. This will complete the scenario. This is very amusing during co-op, when two Arbiters fall in front of the real Arbiter.