Welcome to Android Central! Depends on where you want to buy songs. You can open the Google Play Store, select Music, and purchase a song there, which then gets added to your music library in the cloud. You can access it by opening the Google Play Music app (but be aware that downloading music purchased from Google Play directly to the phone is only accessible by Google Play Music, not the stock Music app). If you want the purchased track to be shown in the stock Music app, it's a little more involved. You have to download the track to your computer from your Google Play Music website, then transfer the file via USB to the phone directory where the rest of your music is located. Keep the conventional folder hierarchy of Artist>Albums>Song.
There are other places where you can buy songs as well, like Amazon. I'm not sure if it's easier to download the music tracks directly to the phone using Amazon.