how to purchase music

Apple Music (the forum you posted in) is a subscription service and is different from the actual iTunes store.

In Apple Music you don't buy songs. You get access to every song for streaming or download for a monthly fee, and yu can just play the song directly by clicking on the play button.

If you want to buy songs, go to the Store section at the top of iTunes.

There you can click once on the song number to get a short a preview, and then click on the price to buy the song.

What "buy" button? There is no buy button. You click on the price. Click on the price once, and you should get a message asking you to confirm the purchase or enter your password if your Apple ID and password if you are not currently logged in.

Also, make sure you are clicking on the "Price" not the arrow next to it.

The Price is the "buy" button. Click on the price to buy the song.

Clicked the buy button, but it does nothing.