Revan wakes up on the Endar Spire at the beginning of the game. Contrary to popular belief, he remembers exactly who he is. The last thing he remembers is Malak's betrayal and the Jedi knocking him out, then waking up here. He quickly figures out others think he's been mind wiped and uses it to his advantage, escaping the Endar Spire with Carth via the escape pod.
What follows is mostly canon for Taris. Carth is his usual self, and Revan acts the way others expect him to act, good and noble soldier that he supposedly is, which is mostly a relief since he's got the perfect excuse to stop acting like a Dark Lord of the Sith for once. There are still a few close calls where he's almost caught doing something he shouldn't have been able to do, but he's able to pass it off as something else or claim ignorance.
Once past the blockade around Taris, Revan knocks out Bastila and Carth and heads straight for the Star Forge, remakes his equipment, and steps back into the role of Dark Lord of the Sith. Bastila is appropriately horrified that the mind wipe didn't work. Revan successfully points out how evil destroying someone's identity over outright killing them is, plus mind tricks don't work on someone unless they're weak minded, which Revan certainly is not.
At the point, Revan needs allies since Malak has betrayed him, and lets the two in on what's actually going on with the True Sith and the fact that he's only pretending to be evil until he can lead an army to the Sith emperor's door. Bastila is disbelieving for a bit, but comes around. Carth is stubborn until it's pointed out Revan had nothing to do with Malak and Karath's actions while the Jedi had him out of commission, and is shown a holocron Revan made to the both of them showing just how bad the Sith Emperor is. Canderous and T3 were already on board really, considering Canderous already suspected and respected Revan anyway. Mission and Zaalbar weren't very hard to convince either, particularly when Revan points out hunting down Malak is on the to-do list.
Unknowing that Revan is already there, Malak returns to the Star Forge and Revan kills him. No taunts, no torture. Just a clean kill. Bastila is once again horrified until Revan is snarky and asks whether he should have mind wiped him like the Jedi tried to do, reminding her of their previous conversation about the evils of the Jedi which promptly shuts her up since she's still reconciling Revan's rather valid points. Revan may not be a Sith, but after what the Jedi did on top of letting the Galaxy to suffer through the Mandalorian wars, he doesn't consider himself a Jedi either.
Thus follows is Revan and crew taking the galaxy by storm on a beefed-up-by-the-Star-Forge Ebon Hawk. Considering Revan was already about to win anyway, and now that he's not holding back against the Jedi out of a sense of obligation, his first move is to move the fleet to Dantooine and invades, rather than glasses the planet like Malak did in game. Revan may be ruthless, but he's not a bastard. Capturing the Jedi council is almost ridiculously easy, along with the rest of the Jedi there. After he's evacuated all the Jedi and people from the area, he glasses the spot, including the map to the Star Forge there so no one can find it but him. He then interrogates the council on some of their actions including what they did to Revan. He executes the ring leaders of those who tried to have him mind wiped and is successful in convincing a spare few of the Jedi council of what's really going on. The rest he simply keeps imprisoned or uses the Star Forge to strip them of their control of the Force depending on their actions.
It's almost ridiculously simple for Revan to take over at that point. He succeeds in taking over the Galaxy with less bloodshed, then turns the might of the Republic and his 'Sith' against the True Sith in the outer rim. What follows is a lot of plot points from KotoR 2 and SWTOR, as well as Revan tracking down HK-47 on Tatooine. I'd write this story myself, but I fear I wouldn't do it justice since I'm not as familiar with KotoR 2 and SWTOR as I'd like.