The factory air filter is not really designed to be cleaned, generally it is replaced. But you could probably blow it out with compressed air if you wanted.
Now, if you have a sprint or k&n type air filter... those can be cleaned. Each manufacturer offers their own cleaning kit.
Actually, the owner's manual calls for the filter to be cleaned every 7500mi, and replaced every 15000. It's listed as an operation that must be performed by the dealer, but it's actually pretty easy to do. When I got my 899 she had ~4000mi on her, but I decided to look at the air filter anyways: it wasn't bad by any means, but I got quite a bit of dirt out, both trapped inside the filter itself and sitting on the dirty side of the airbox.
To clean the filter, tap it gently on a flat surface, dirty side down, to get the big stuff out, then blow it with compressed air from the clean side. When you got no more dirt/dust coming out, you can then blow it freely on both sides.
To clean the airbox, do NOT blow compressed air there, or dirt will go on the clean side of the airbox. Instead, cover the intakes with clean rags as a precaution, then go in with a vacuum to remove any loose dirt, especially around the steering column. Finally, use a damp microfiber rag and clean everything well, being careful not to drag any dirt into the clean side of the box.
In the photo below, I had just cleaned the box with the vacuum, but still had to use the rag... you can still see some dirt marks (caused by water, it seems) on the side and on the bottom.