Start by finding the user manual on the Internet. There are free downloads. And there are maintenance videos on YouTube. (It's usually called the Touch and Sew)

CLEAN it ... inside and out. I spray WD-40 liberally on all the gears and moving parts whiles slowly moving things manually (machine is UNPLUGGED!) and mop up the excess.

Then do all the maintenance that a user is supposed to do, including lubricating.

Then do a bunch of straight sewing, with a needle but no thread, on some scraps until the lubrication is really worked into the gears.

You may have to clean out more dirty oil and relubricate it the machine was really piggy.

When it sews nicely as a straight-stitch machine, try the simple zig-zag stitch ... altering the length and then the width. Move the knobs or levers back and forth gently until they move smoothly, then sew slowly on clean cloth. Move on to the next knob.

http://www.sewusa.com/Sewing_Machine_Repair/Singer_Sewing_Machine_maintenance/Singer_603.htm 

Shows where all the cleaning and oiling points are