The lens on your digital camera is somewhat delicate and deserves special treatment, so we'll get to that component on the next page. In the meantime, realize that the body and accessories of your camera require cleaning, too.
Let's start from the outside and work our way into the camera. Understand that your camera spends most of its time in a nice soft padded case. Whether that case is pocket- or suitcase-sized makes no difference -- but if you heavily use this case, it'll get dirty.
If you use a small case, you can remove all of your camera's accessories and swish the carrying case around in a sink or bathtub. You might be taken aback at how much dirt darkens the water. Use a fan to dry the case. For larger cases, you may need to use just a damp sponge or cloth to wipe the interior.
Now you'll want to clean the body of the camera itself. There are probably a lot of fingerprints and maybe even some accumulated oily dirt jammed into the cracks of your camera.
Use a small cleaning brush to clear away excess dirt from the camera exterior. You'll find these brushes at camera stores and superstores. The brushes often come equipped with rubber bulbs that let you use puffs of air to remove dust (always avoid using canned air for this purpose because it's far too powerful, uses liquid propellants and may cause more harm than good).
Use a soft cloth to wipe away remaining grime. A microfiber cloth specifically made for camera lenses works great; don't use microfiber cloths made for eyeglasses. Apply a tiny bit of moisture if necessary, but only to remove tough grunge.
Don't invest in cleaning chemicals for your camera unless your camera's manufacturer instructs you to. Not only are these chemicals pricey, they can damage your camera's surfaces if used improperly.
If you own an SLR digital camera, you probably already know that you're exposing the image sensor to dust and debris every time you switch lenses. Many contemporary SLRs have sophisticated sensor-cleaning routines they use to keep the sensor clean without any action on your part. However, once in a while, stubborn dirt appears on the sensor (and subsequently, your images) and you must remove it.
Because every SLR is different, you'll need to use the Internet for specific sensor cleaning instructions for your particular model. But the basic process is usually the same. You'll have to engage a special cleaning mode on your camera, and then use a sensor-cleaning brush (also available from many online vendors) to carefully snag dirt from the sensor.
Sensor cleaning is a touchy process and if you're too rough you can actually damage the camera if you're not careful. But with a bit of research you can confidently clean the sensor yourself without paying ridiculously high professional cleaning fees.