The most important part of a light fixture is the one nobody looks at: the antique lamp socket. The socket holds the bulb and delivers the current, so it's where the actual electrical work happens. The fixture around it is a frame; the socket is the machine. And it changed more, and matters more, than its size suggests.
Bases and materials
Early sockets came in materials that show their age: brass, porcelain, early composition, and in a range of base sizes before the market standardized. The medium base, the common household size, won out for most fixtures, but the mogul base, larger and built for higher wattage, held its place in torchieres, big table lamps, and anywhere serious light was needed. Knowing which base a fixture takes is the first practical fact about it.
Control at the socket
The socket also carried the controls. Many old fixtures switched at the socket itself: the pull-chain socket, the turn-key socket, the push-through. These put the control at the fixture rather than on the wall, which is why an old lamp often turns on with a chain or a key. When one fails it's usually the socket, not the fixture, that's worn out. Porcelain sockets deserve a note: because porcelain takes heat far better than plastic, a porcelain socket handles high-wattage and enclosed fixtures that would cook a modern plastic one.
Salvager's Note: Replacing a socket? Match three things: the base size (medium or mogul), the wattage the fixture runs, and the control (pull-chain, keyed, or plain). For anything hot or enclosed, choose porcelain over plastic.