transformer check

Hey everyone, Im new here, I have an above ground swimming pool with a pool light that illuminates the inside of the pool, the light has stopped working, I don't know if it is the bulb or the transformer, since the transformer have been known to burn out over time, it is 12 years old. One end of the power source plugs into a GFI on the side of my garage, the wire runs to the transformer then the wire goes to the light at the pool, when I disconnect the wiring to the bulb it has two connections one black one white, these plug into two connections connected the the light housing two yellow connectors.
I do have a new multi meter, but Im don't know how to use it very well, can someone explain how to check to see if power is getting to the connectors to confirm if my transformer is good, please be specific, what setting on the multi meter, what color probes to touch where, I would appreciate it. Thanks!