In reply to Mountain Llama: Use levelling compound a day or two before you start tiling, that way you're not messing around with extra glue and faffing around with sorting the levels out. It's dead easy to mix and use -make a watery mix and roughly spread it around with a plastering trowel - the compound will do all the rest and the you're left with a uniformly flat area to tile - much faster.
If you tile around the depressed area before returning to fill it in then it's too easy to make a mistake with the setting of the surrounding tiles, then you're stuffed.
How thick are the tiles? Normally floor tiles are around 8-10mm thick, the thinner they are the weaker they are. I used slate tiles for my hallway, and they're a proper pain because they are all varying thicknesses! It is invariably a good idea to glue up both the floor and the back of the tile, this also gives you a bit of play if the tiles vary in thickness.
Sound silly but hoover the floor first, remember too to seal / prime the floor with a PVA and water mix - this will enable the adhesive to bond much better. I usually prime a few square metres at at time and then start tiling as I find the tiles have a stronger bond to the floor.
Sorry I've been overly verbose but I hope there's some useful info in there that you can use. I'm happy to help if I can and you're welcome to PM me if you wish.