Originally posted by Class A As Arpe said. Here's my detailed procedure:
- Loosen rear cap on new lens.
- Put lens cap on old lens and unmount old lens, camera facing down.
- Swap rear cap from new lens to old lens.
- Mount new lens to camera, camera still facing down.
- Start breathing again...
It is good practice to keep (front and rear) lens caps clean as any dirt will transfer to the lens and from their potentially into the camera.
I recently started changing lenses somewhat like this and it has dramatically reduced sensor dust.