li10up's advice is good. Chain, chainrings, cassette and brake pads are parts that wear out and need to be replace periodically, though chainrings should last a long time and could be expensive. Check that the frame is without cracks or dents and no major scratches. Look carefully for any indications of bends in the frame or a previous accident. Look from the front, back, and side to see that things look straight and aligned. Fork blades can be bend backwards from an impact. A test ride is helpful here - the bike should ride straight without a tendency to turn even if you release the bars briefly. Also check the bearings for smoothness and lack of play. Remove each wheel from the bike and turn the axle by hand - it should feel smooth without any notches and it should turn very freely but without any side-to-side play. Spin the wheel while holding the axle ends in your hands - it should keep turning for a long time. Remove the chain from the chainrings (drop it between the crank and the frame) and spin the crank. It should spin freely and smoothly and have no play.
Also a good idea to find out the age of the bike and availability of parts for it.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72