Rewiring socket for lamp question
Assuming that the lamp cord is polarized you want to make sure that the hot side of the two wire conductor is attached to the center (copper) terminal on the socket. The common side of the cord is connected to the outer (silver) terminal.
The hot side is the one that plugs into the narrow slot in a polarized receptacle. The wider plug blade can only fit in the wider slot on the receptacle and is the common or neutral wire. You can also tell hot from common by feeling both sides of the lamp cord. One side is smooth (hot side) the other side is usually ribbed (common or neutral side).
You also want to make sure that the the screws are sufficiently tightened.
If the plug on the lamp cord isn't polarized with a wide blade or prong on one side and a narrower blade on the other you should replace the plug or the entire lamp cord with one that is polarized.