Best Way to Clean an Unprotected Image Sensor

Not with a cotton swab!

You should buy the correct sensor swab for your particular sensor. Here is an example from Amazon.

You must use the correct fluid (I use Eclipse) and follow through with one continuos swipe across the sensor. Do not use the same side of the swab twice!

The swab should be the exact same width as the sensor.

If you are lucky what looks like scratches may only be lines from the cleaning solution.

Yes, I'd agree with this, and add: use an optical-grade can of compressed air to carefully blow off any dust first. Keep the can well away, initially, then bring it's nozzle in closer to about six to ten inches from the surface. If you're not sure it's optical grade compressed air, aim it at a mirror and see if it leaves any residue; if not it should be ok.

Use very light pressure (like almost none) when wiping. Let the solution do the cleaning.

If the cleaning solution leaves a residue, you can 'fog' the surface with your breath, then wipe it again with a clean swab. (That may sound odd, but it's a method used by German lensmakers for a final cleaning of high grade lenses.)

No, no, no.

The propellant in many of those cans can leave a residue. Don't take a chance.

A better solution is the Rocket by Giottos.

Also, keep it in a zip lock bag when not in use.

Have a close look at the sensor, it may have a layer of plastic micro lenses on top in which case it will stand more handling than a bare sensor.

Whatever you do be careful not to touch any of the bond wires surrounding the sensor, these are delicate & if you break one, the sensor is scrap.