Pinkberrykay,
I have a small business cleaning and maintaining Featherweights, been doing for about 10 years and have 4 featherweights of my own.
When I clean a Featherweight; I use the blue shop paper towels you find at Wal-Mart and a bamboo skewer to clean all the old grease off of the gears on the top and bottom of the machine. When its clean, I put new Singer Lube on the gears, just squeeze a bit on your finger and smear it on the gears, turning the hand wheel toward you so that you get the entire gear. You'll also need to put Singer Lube in the grease ports in the motor; NEVER any oil in the motor.
Put 1 drop of sewing machine oil in each of the oil holes and wherever else your manual shows you.
Sharon W. in Texas