Get into the habit of taking care of your equipment: that way, you will avoid any nasty surprises! And even better, it will last longer!
Follow the instructions, which will depend on the specific cleaning system in question. If you are unsure about performing the cleaning yourself, a camera specialist will be happy to provide this service!
To combat greasy dust:
pre-saturated swabs for cleaning the sensor. - cleaning kits with spatula tools for wet-cleaning (with cleaner liquid included)
For dry dust:
use a dust blower (available from pharmacies) with the reflex chamber pointing downwards to release any dust. Do not touch the sensor while blowing. Sensor cleaning swabs. Compressed air canisters suitable for blowing or vacuuming any dust off the lens. Special dust removal styluses for removing dust from the corners.
Remember: even the thinnest layer of dust will have an impact on image quality. But there is no point in going crazy over a single speck of dust.