How do you hard wire a lamp socket to the ceiling?
This is assumes we're talking a screw in bulb socket like a medium base A26.  You can adapt the below for other socket types.

The first thing to do is test the socket itself.  Best way to do this is to use 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 socket itself.   If it reads the correct voltage, either your bulbs are bad or they are not making contact with the socket.  With the power off, try using a screw driver to gently lift the bottom pin up a bit and then try your bulb again.