1. patience! - allow lots of time (several hours).
2. a set of artists brushes to loosen the dust. I used six, sized from no. 3 up to no. 20. A stiff bristle is best. Work the brush between the larger string gaps, taking care not to inadvertently do any 'tuning' by bending on the strings.
3. a really sucky vacuum cleaner. While carefully dusting between the strings with the brush have the vacuum cleaner going at maximum, using the upholstery nozzle. Unless you have an industrial strength vacuum cleaner it is probably a good idea to give it a rest after each half hour, so you don't fry its motor.
4. an old broomstick is handy to prop the lid up high enough to allow you to 'get under the bonnet'. Make sure it can't let the lid fall (as the weight would probably dice your head through the strings!)
5. be very careful when dusting the top of the dampers, as they can be easily bent.
6. the soundboard under where the strings cross is hard to reach. I used a very small rag attached to the end of some electrical cable to reach under the strings to clean this bit.
and here is the result - a 1988 piano that looks like new: