As mentioned, read up on headsets on Sheldon Brown and the Park websites. The next step is to disassemble and inspect the headset, fork and headtube. Assuming the headtube and fork are in good shape, I would think it highly likely that you will need to replace the headset. That old and having sat outdoors chances are that the headset is corroded. If it was heavily greased in days gone by, there is a chance you could get by with cleaning it up, putting in new bearings and grease, and properly adjusting it. Since the headset is that loose and it was left outdoors, I'm guessing this bike was not that well cared for.
New headsets can be purchased for anywhere from $15-45 at your LBS or online. My suggestion is to get it at the LBS, both to support local business and to assure you get an appropriate headset.