I mentioned this elsewhere, but the aggressively simple answer is that it still works pretty much the same as current launch technology: the big huge rocket get

I mentioned this elsewhere, but the aggressively simple answer is that it still works pretty much the same as current launch technology: the big huge rocket gets the payload onto an appropriately high suborbital trajectory, and then the payload use its own (much smaller) rocket to circularize the orbit. They're replacing the launch vehicle with a centrifuge, but otherwise the mission architecture remains broadly similar. The launch vehicle only getting things onto a suborbital trajectory is a key reason why SpaceX recovering Falcon 9s is possible. They are not making a round trip around the planet before coming back, which would be necessary if it were actually doing orbital insertion too since the circularization burn happens a decent chunk of the way around the planet from the launch site. It would also be insanely wasteful; the fuel needed to get that whole giant chunk of steel up to orbital velocity would be vastly greater than the cost of just putting a small orbital maneuvering engine on the orbital vehicle so that it can finish the job for itself. And as an added bonus the spacecraft also gets to use that engine for general-purpose orbital maneuvering. The Space Shuttle did something similar. Those huge main engines only got the orbiter onto a sub-orbital trajectory, too. They'd then jettison the external fuel tank while still on a sub-orbital trajectory (helpful for reducing how much space junk you produce), and use the OMS for orbital insertion. You really don't need such a big engine for this part of it, anyway. The SSME produced about 150x as much vacuum thrust as the OMS.