I just remove the fan and use a brush to remove the dust, and a vacuum to evict it from the case. After cleaning the fan blades, I remount the fan.
If you have severe 'baked-on' contaminant problems, get some alcohol to clean the heatsink and fan, and some heat sink paste to recouple it to the processor. Remove the fan and heatsink from the processor, disassemble, clean the heatsink and fan, reassemble fan and heatsink assembly, wipe excess or dried paste from the processor, put a dab of new paste on the processor, and re-install the heat sink assembly.