As tempting as using Pepsi Max might be....
The sloping mirror is common to all SLR (Single Lens Reflex) cameras. It ensures the image you are viewing is exactly what the film/sensor will get, since it uses the same lens. With film cameras - this was the only way to get exactly the shot the photographer saw - no parallax error and no approximations for zoom lenses.
Also, by using an optical path for your viewfinder, there is no power needed for you to see the subject. As well, the main image sensor is protected until the shot is taken, when the mirror flips up out of the way for that instant and then drops back down.
The mirror only serves to reflect an image to the viewfinder, so any dust or other contamination will not affect the image captured. HOWEVER, it is precisely positioned so that the viewfinder screen is exactly the same distance from the lens as the digital sensor - so when you focus in the viewfinder, the captured image is also in focus. Contamination on the mirror may affect the ability to focus.
As for cleaning it - Step 1 - Read the Manual! It should be done with great care - at least that's how I approach it. It is mounted on a relatively lightweight mechanism, so that it can move quickly and any excessive pressure could affect its position or movement. If unsure, I might suggest you pop into a reputable photographic store when you have some spare time and run through a couple of these questions with someone who knows what they are talking about. If you have questions, you can always raise them here.
By far the better way is to PREVENT contamination from getting into that area in the first place. These are some practices I follow:
1. Keep a lens ON the camera. This not only protects the mirror (and sensor!) from contamination getting in, but also means you can just pick up the camera and shoot, if your opportunity for a shot is short.
2. When storing lenses, keep a lens cap on the front AND rear of each lens to protect both pieces of exposed glass from contamination. This will also reduce the dust introduced into the body when a lens is fitted.
3. If you have to remove the lens from your camera for any length of time (and I'm talking minutes and upwards) fit a body cap to the camera body (like a lens cap - but covering the hole where the lens is mounted) to keep out contamination.
4. When changing lenses,
(a) make sure (if at all possible) you are not in a place where dust, water or other contaminants are prevalent. If you can't help it, try and be as protective as possible.
(b) Before removing any rear lens caps or body caps, giving a quick once over with a blower brush will never go astray.
(c) Between the time the first lens is removed and the second lens fitted, lay the camera body face down on a dust-free, lint-free surface. (If it's going to be exposed for any length of time, fit your body cap. Dust floats down more than up - but a wayward grain of sand (or a precision bombing seagull) will be a problem if it finds a target inside the camera body. The risk of this is very small - but a simple change in orientation makes it infinitesimal.
One last thing, while we are talking about protecting lenses and such ... for any camera that can take filters, go get yourself something like a Skylight 1a filter and keep it permanently on your lens. Its effect is very subtle, but improves skies and clouds just that little... It hardly makes any difference to exposure and you can confidently ignore the fact that it's even there - BUT - If you get a scratch ... it's much better that it is on a relatively cheap filter (which you could remove and keep shooting) than on your more expensive lens! Also, cleaning a filter is easier than cleaning a lens!