There is no single "best" method of sensor cleaning.
In fact, for a proper cleaning, several steps using different methods are very likely to be needed.
Among the tools I use to clean sensors is a product called "Speck Grabber" which is similar to what's been mentioned here, but has a tiny, precision point and is intended to remove stubborn, individual specks of dust.
I've also used Dust-Aid, which are single use pads that are the same idea, a "gentle" adhesive that lifts off dust specks... is pressed lightly onto the sensor surface, not dragged across it.
Sometimes I use a vacuum, too (
very carefully, they can do damage if used too close to DSLR shutters and mirrors).
Also an anti-static brush, to coax loose adhered dust.
But none of those will remove oils that get onto sensor surfaces from shutters and other mechanisms. For that a "wet cleaning" with a swab is the only thing that will work (actually, it's more of a "damp cleaning", since the swab shouldn't be too wet).
And, after a wet cleaning, very often a Sensor Pen is needed to remove a slight haze left by the cleaning solution. Gently polishing with the pen also helps the surface to be more resistant to dust adhering to it again in the future.
More info about sensor cleaning, from people who actually do it for a living:
www.cleaningdigitalcameras.comAttached is a sensor cleaning "flow chart" from the above site...