Join Date: Oct 2004
Location: Florence, KY
Bikes: 1954 Hetchins M.O., 1959 Viking Severn Valley, 1970 Raleigh Pro, 1972 Fuji "The Finest", 1974 Raleigh Superbe&Comp, 1976 Raleigh Team Pro, 1996 Giant Iguana, 2000 Bob Jackson Arrowhead
Are you familiar with Sheldon Brown's websites, and with the ParkTool website? A lot of what you might need to know to work on a bike can be found in these places.
The usual things to check are the wheels (are they true? how are the braking surfaces? Do they spin freely?), tubes and tires, the brakes (cables, housings, adjustment, pad condition), the shifters and derailleurs, the chain, crankset and headset. It sounds like it wouldn't hurt you to service your headset.
In search of what to search for.