To the extent that small numbers of dust particles can be fairly conveniently dealt with in post-process (or perhaps ignored altogether in some cases), a method for cleaning your sensor which isn’t 100% effective, but is very easy to perform and tends to remove most dust, may be a reasonable one to adopt for day-to-day maintenance.  For longer-term maintenance, I recommend sending your camera in to the manufacturer yearly for a thorough cleaning; this may take a week or more and will typically result in a small surcharge. 
    For day-to-day cleaning of the imaging sensor, I recommend using a high-quality air blower, such as the Rocket Blower by Giottos.  The idea is to use a low-pressure gust of air to dislodge any particles loosely adhering to the imaging sensor. 




Be careful when doing this not to insert the blower’s nozzle into the mirror box, because if you accidentally make contact between the blower and the sensor, you could damage the sensor’s outer filter.  Also, be sure to use a quality blower rather than a simple rubber air blower meant for cleaning lenses.  A quality blower like Giottos’ Rocket Blower will have a built-in filter to keep the blower from blowing particles onto the sensor (which could make the sensor dirtier than it was in the first place).  Also, avoid using cans of pressurized air, since these may emit chemicals or vapors which can collect on the sensor’s surface and possibly degrade image quality or even permanently damage your sensor.



    For particles that refuse to budge when blasted with low-pressure air, a wet or dry contact method may be necessary.  The materials needed for these types of cleaning are readily available for purchase over the internet.  Be aware, however, that performing these types of cleaning yourself may void the warranty on your camera, and may possibly even cause irreparable damage to your imaging sensor or mirror.  If you don’t feel comfortable assuming these responsibilities, I highly recommend that you let a professional service your equipment instead of trying to do so yourself.  In the latter case, it’s always best to deal with the original manufacturer of your camera; I’ve paid substantial sums of money to third parties to clean my cameras, only to find that the imaging sensor came back as dirty as (or possibly dirtier than) before the service was performed.
    If you decide to clean the sensor yourself, you’ll need to buy a specialized sensor cleaning kit.  I bought the one shown below for about $25 (US).




The kit shown above includes cleaning elements for the sensor as well as for the rest of the camera and also for lenses; be careful not to use anything intended for lenses or other camera parts on your sensor.  In this particular kit, the swabs shown in the center and the bottle of cleaning fluid on the left are intended for use on the sensor.  The swabs and even the cleaning fluid come in different sizes and formulations, and you need to use the right ones for your particular camera model.  If you use a brush intended for a larger sensor size than what’s in your camera, you can end up inadvertently wiping lubricants or other filth that collects around the sensor’s periphery onto the sensor itself, and these can be very difficult to remove once they’re on the sensor. 
    Be sure to follow the directions in the cleaning kit very carefully.  Some makers of cleaning kits will guarantee that their kit won’t damage your sensor, as long as it’s used properly.  Some even offer a warranty involving reimbursement for certain types of damage resulting from the use of their product.  Keep in mind that what you’re actually cleaning isn’t really the imaging sensor, but the glass filter (sometimes called an IR filter or an antialiasing filter) that covers the sensor.  If you damage the filter, it can typically be replaced by the manufacturer without having to replace the (much more expensive) imaging sensor itself.  In any event, it’s a good idea to read the fine print on any guarantee from makers of cleaning kits, to see exactly what type of damage they cover.
    In addition to wet-cleaning kits, which use a liquid solvent to wash the sensor, there are also dry-cleaning kits, which provide fine-tipped brushes to collect the dust via a static charge on the brush.  If you’re traveling on a commercial airline, you may want to investigate these dry-cleaning methods, since the wet-cleaning methods generally involve the use of a flammable solvent that currently is not permitted onboard commercial aircrafts in the U.S.
    While you’re cleaning the sensor (or just blowing off the dust with a Rocket Blower), you may be tempted to also clean the front surface of the main mirror.  Note that the mirror in a DSLR can be very, very fragile.  The mirror itself is coated on the front (not on the back, as in household mirrors) with a delicate reflective coating, which can be scratched even more easily that the filter on an imaging sensor.  Also, applying too much pressure to the mirror can damage the mechanism which flips up the mirror during normal DSLR operation.  Nevertheless, a clean mirror is important: although the light path for exposure does not pass through the mirror, the light paths for autofocus and metering do pass through the mirror, and could conceivably be affected by any dirt that’s in the way.  Some cleaning kits for imaging sensors can also be used (gently) to clean the mirror, but you should only do so after reading the directions and verifying that the kit is recommended for cleaning mirrors.  As with sensor cleaning, I recommend letting a professional clean your mirror; the original manufacturer of your camera should be able to do this for a reasonable fee.
    Finally, it goes without saying that it’s best to try to keep dust out of the mirror box so that the sensor (and mirror) don’t get dirty in the first place.  When changing lenses, point the camera downward, and don’t allow the mirror box to remain open for long periods of time.  Avoid changing lenses in dusty and/or windy environments, if possible.  Also, be sure to remove any dust from the mount area on the lens before mounting the lens, since this dust can then find its way onto the imaging sensor.  Likewise, if you keep your lens caps (the ones that cover the lens mount, either on the lens or on the camera body) in your pocket, make sure they don’t get dusty or covered with pocket lint, because this too can travel, directly or indirectly, into the mirror box and onto the sensor.  With a self-cleaning sensor, a Rocket Blower, and some common sense, you should be able to get by with no more than a yearly wet-cleaning of the sensor, preferably performed by the camera’s manufacturer.