You will need either a continuity tester or a multimeter in the Ohms mode.
The continuity tester uses a battery and light and connections.
And heere are a couple of multi-meters.
Here are a couple of articles aobut using a continuity tester.
You want to disconnect the blue wire at the ceiling to prevent confusing with it meausring the fan motor instead of the lights.
The first thing that you want to do is to check across the switch. It might be bad.
Then the neutral wire (white) to the shell of the socket(s). The shell is the outter part that the bulb threads into.
Then check from the blue wiring at the ceiling to one side of the switch. Then the other side of the switch to the tang in the center of the light socket.
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