Well, if its a ceiling that is going to lead you to the attic, be prepared to get dirty!
I took mine off, and had a wet&dry vac and sucked out all the coal dust from the rafters as I knocked down the ceiling.
An older house, its probably plaster and lathe, which will be dirty and dusty. Try and take it down in sections, (if you have a saw-zall, then use that to cut between the rafters to take it down in chunks, easier to get rid of that way, or its just going to be even more of a mess if you just knock it down all over the place.
Put plastic on all the doorways. Plastic on the floor and move every piece of furniture out of the room! Have a fan blowing in one window, and out the other window because of the dust.
If your lucky and its gypsum board, you can take it down in large chunks. The larger the better.
Wear proper protection, dust mask, (a good one), long sleeve shirt, a knit cap and hard shoes! (remember, if you take it down, the nails should be gotten rid of as soon as possible so no one steps on them and gets hurt!). Keep kids out of the area!!
Ok, now for putting up the new ceiling, go rent one of those nifty machines from a "rent-all" place, that lifts up drywall...(They are a friend to whom ever has to do this sort of work, or just get a large bunch of guys together and have them hold the thing up while you sccrew the wall board to the ceiling...Not a plesant way to spend a day).
I dunno, last time I heard they were about 12 bucks for 4 hours or so, but it may vary in different locations...
Some sites to help you with the drywalling...
Hope this helps... Others will probably have better ideas, but, these are just mine
Just my two cents for what its worth, and a wee bit extra for the collection plate...