Congrats on a great gift! Your machine looks like it's in great shape. It won't take much at all to get it ready to sew again. As far as cleaning it, Joe nailed it. Also check out the sticky on cleaning old machines.
The plated parts can be cleaned easily with alcohol to dissolve old dried on oil. Just be sure NOT to get it near the machine itself. Alcohol dissolves shellac and will damage your finish.
New leather treadle belts are still available.
Your machine is a model 66. You can download a free manual at Singerco.com. You can find out how old it is here:
http://ismacs.net/singer_sewing_mach...-database.html
Glenn also has a very good tutorial on restoring the finish on the woodwork. It's in the tutorials section.
I hope this helps,
Rodney