installing bathroom exhaust fan in drop ceiling
There's really no extension involved. You'd suspend the fan flush with the drop ceiling tile as you normally would with drywall. The specific hardware used depends on the fan. You could DIY by simply adding metal or wooden crossbars with sheet metal screws to the fan housing that rest on the tile and extend over the grid rails. Some kits may offer bars similar to what you'd get with a recessed light canister.

You'd also need to create clearance in the drywall ceiling. If there's no insulation there, that's easy. Just give yourself enough room to work and hack out a rectangle. 

If you're in an insulated ceiling you'll need to box it out and be sure to replace the insulation above, along with any vapor barrier present.