how to change a light socket? There are typically two or three screws holding the fixture itself to the bracket. Lower the fixture down, exposing the wire light socket. Once the fixture is down, use your hands or pliers to undo the wire nuts.
Wire nuts are the plastic cone-looking pieces covering the ends of where the wires come together, connecting the black and white wires coming from the fixture to the wires coming from the ceiling. There might also be a ground wire from the fixture attached to the metal of the junction box in the ceiling by a screw.
The first thing to do is test the lamp holder itself. The easy way try this is to apply a multi-meter set to AC and an appropriate voltage setting for your supply voltage. Using the test leads, touch the bottom pin and the metal of the base exterior (the part the bulb screws into). It should read your supply voltage.
If it does not then there is an issue with the lamp socket itself. If it reads the right voltage, either your bulbs are bad or they aren’t contacting with the socket. With the turn off, make use of a screw driver to gently lift the bottom pin up a bit and then try your bulb again.