First thing to establish is are you entitled to take it down in the first place! It seems obvious but is it a semi -detached or terraced house? - if so the chimney stack may well be shared with your neighbour - in which case you can't really do anything to it!
Assuming that the chimney stack serves you only, and again this seems obvious, you start at the top and work down. This is a big enough job and not really for a DIYer. You're going to need scaffolding and ladders for safe means of access and egress to the chimney stack to be demolished. Even on a bungalow this involves a fair bit of scaffolding, as the area around the stack should be decked out with proper guardrails, toeboards etc. You need a way of getting the rubble down off the roof - a chute might be a good idea. The demolition is going to require a breaker (i.e. a kango hammer) unless the chimney is in such bad condition that you can use a lump hammer and cold chisel or a sledge hammer to break it up. It needs to be broken carefully. When you have taken the stack down below roof level, you are going to have to roof over the opening and weather the roof properly again. This is going to involve inserting at least 2 new rafters each side (assuming its an A roof) and a infill piece of ridge board. The gap will have to be felted and the laths or battens carried across the gap. Tiles or slates to match the existing on the roof have to be fixed in position. Doing this with old blue bangor slates for example is very messy, as it is easy to break more slates in the process. At least 2 new ridge tiles will need to be got (the right angle for the pitch of your roof) and bedded in cement mortar and pointed. (This assumes chimney rises through ridgeline but it could also be at an intermediate position on the slope, in which case the ridge is not affected).
This is a job which needs an adequate number of men to get it done quickly (as you want to get your roof weathered again quickly).
You might also have to think about the rest of the stack below loft level - i.e. any downstairs fireplaces may need to be sealed off to prevent fires being lit when there is no flue to the outside!
Hope that helps!
JD
January 2008