Readers Digest Condensed version:
Check the alignment by sighting along both edges of the presser foot and the edges of the feed dogs. They should be parallel.
If not and everything else is OK: presser foot height and presser foot lift lever slack, then you simply remove the face plate and loosen the presser foot shaft screw just enough so the shaft can be turned, then align the foot and dogs. After that retighten the lock screw.
Different machines vary but this is mostly the same.
The one thing I've seen on 66s and other Singers is someone has messed with the foot height adjustment creating a gap between the needle plate and presser foot when the foot is all the way down, and you just cannot get the proper foot to feed dog pressure. At that point the material will twist and turn no matter how tight you crank down the presser foot tension knob.
Joe