They request microwave as it's a different procedure to the others. It usually gets asked for in/approaching the hold so atc know who's doing what approach and the crew can brief and configure the aircraft accordingly. In terms of what it looks like to atc, pretty much the same as an ILS approach. So it guides them to the runway threshold, from anywhere up to around 15nm out, and is approved by Director. They don't get landing clearance until they're inside 2nm, which comes from the tower.
In short, landing clearance comes (a long time!) after clearance to follow an ILS/MLS/Whatever approach.