Compressed air.
Just open the PC up, blast it with the air to get rid of all the surface dust, then blast areas where dust builds up (fans, heatsinks, dust filters) more thoroughly. It's a good idea to hold fans still when you blast them to prevent them from spinning up too fast and damaging the bearing.
That should get rid of at least 70% of the dust in an average PC for an outlay of about £3 and 10 minutes.
Step 1 in this is
1) wait for misses to go out so she does not witness cloud of dust
Also a Microfiber cloth to wipe the case panels down with etc.
Couldn't it be dangerous when cleaning with a brush? Would it short circuit the components?
No, but even so the computer should be off when you do this
How about the static being generated?
Compressed air cans, paint brushes (1/2" and a 2" size), vacuum cleaner brush attachment.