Headphone set plugged into Lenovo Desktop does not work, what am I doing wrong?

Headset (with microphone) or "Headphone set"?
If with microphone, you are plugging in an incompatible plug into the headphone socket. Won't work. You need a headset adapter that does one socket to two plugs--one for headphones, one for microphone.

Probably need to set it as default output using the audio mixer by right clicking the audio icon

Ba a

Have you got the head phones plugged into the out put plug?

computers usually have just three plugins for sound. One input, one out put and one for the microphone. Make sure its plugged in all the way in the output plug ib. If no sound either the wires on your head phones are bad or the settings for sound does not have sound going out the output plug in.

You may need a new headset.