Bicycle Mechanics - 1970 Schwinn Sprint rebuild

I am new to rebuilding bikes. I ride a new mountain bike but have never worked on an old one. Is this schwinn supposed to be able to free wheel? Right now if I turn the back wheel the pedals turn.
It sat in a garage for 30 years or so but its functional in all other aspects. Gears change brakes work, sort of. Just the free wheel has me confused.

If it has multiple gears, it's almost certainly supposed to freewheel. Fixed-wheel bikes with gears are very, very uncommon (there are a handful of internal hub gear systems that let you do it). I'd imagine the freewheel is gunked up with old oil/grease. Is it an internally geared hub or does it have multiple sprockets on the outside of the hub?

The cluster of cogs on the back wheel is called a "freewheel". Yours is all gunked up. New ones aren't too expensive but it takes a special tool to take off the old one.

If you feel like you hve nothing to lose you can try to take the old one apart but I don't recommend it. The freewheel is full of real little ball bearings and itty bitty springs.

Thanks fellas. I will try to grease it up. It was sitting in a garage for 20 years, so I hope its just a little grease needed. I will maybe use the yellow bike peeps we have here in Austin if needed.

DO NOT grease it up or take it apart - greasing will not remove old grease that is hardened, and disassembly is out of the question - time intensive, likely to lose bearings or parts. Best to have a shop remove the freewheel (don't remove any guards or spacers underneath the freeewheel). Dunk it in solvent and spin until it runs free, then just follow Sheldon's lubrication advice: http://sheldonbrown.com/freewheels.html and reinstall it if it now works OK - no tool required, just carefully screw it on. (handy hint - turn it counterclockwise until it seats into the entry threads, then clockwise til it stops. Riding will tighten it.