Here's a picture of a bobbin winder clutch. It's on the handwheel of this old Kenmore. First, loosen the small screw on the center knob. You don't have to take it all the way out, just loosen it. Then twist the center knob to the left (righty-tighty, lefty-loosey) until it comes off. This is a picture of what you'll see under the knob. Can you see the metal ring that's sitting on the center shaft? Remove it.
You may need to take the top lid and/or the side panel off to allow the handwheel to move in and out. If you're not sure you can get the belt back on correctly, you don't need to take the belt off, just loosen the outer panels so you can move the handwheel on it's shaft, like this...
Can you see how the center shaft has moved back inside, as I push the handwheel out? Use some "solvent" (WD-40) to remove the old, gummy oil on the shaft. Squirt it inside the hole and work the handwheel around until the gum is dissolved. Then wipe out as much of the solvent as you can. If you have a can of air, you can blow it out -- we use an air compressor at the shop. Also use the solvent to wipe the old oil off of the metal ring and center knob.
Put 2 drops of oil on the shaft and put the machine back together.
The metal ring under the knob will have 2 or 3 raised nubs on the inside.
Run the machine and see if it's doing what it's supposed to do.
If the machine isn't working well with the ring in its current position, turn it counter-clock-wise one position. Screw the center knob back on and tighten the little screw.
That should take care of it!