Having had my head in a few ceilings I can tell you how they fasten them.  Basically they either drill holes through the vegas, knock holes in the red 'pots' or fix hooks to the underside of the floor above.  They then suspend the tiles on wires. To stop them moving they dunk some straw (grass or fiber of some sort) in yeso and dollop it onto the top and bottom anchor points and between adjoining tiles. The tiles should have some form of metal hook or bar in the corners to allow you to suspend them.

To allow access at a future point in time you can cut the tongues off of one tile (plus its adjoining tiles) and yeso a couple of wooden bars across it. This you can manipulate through the hole and lower into place. I've had to cut through a few where this hasn't been done - quite messy and prone to the tile breaking.

Hope this helps!

Nigel