There are several places and ways you might want to use music in your audio drama: as a theme tune or intro/outro to your piece, as source music from objects and locations within your drama, as an underscore to dramatic scenes to heighten the mood, or as 'stings' to indicate a change of scenes.
This sets the whole tone of your show and it's the first thing that listeners will hear (unless you bring in the theme tune after an initial, gripping scene), so it's arguably the most important piece of music. Often you'll want a title voice-over during it, so lower the volume slightly under that, before swelling again and fading out.
Shows vary in what they use under closing credits. Some use the opening theme again, some use a separate closing theme, and some use a different track every episode to reflect the mood.
These were used a lot in Old Time Radio, and still have a place in modern shows, too. They could be a short phrase or even just a chord - perhaps a discordant one if the mood was tense! Nowadays, they are also a great opportunity for electronic sounds, too, depending on your show.
This is music that happens within your storyline. It's music that the characters can hear (or make), so it includes things like car radios, background music in locations they visit, or even instruments they play if it's part of the action and others know that they're doing it. So in a film like Casablanca, Sam's piano playing is diegetic - the characters listen to it and respond to it.
If you use this kind of music, you may need to play around with it to indicate its source. For example, if your character turns on the car stereo you might want to split the music into two tracks and pan each of them hard left and right, as if it's coming from speakers in the doors. You could run it through a high pass filter to make it sound a little tinnier.
In each case, think about where the sound is coming from in relation to your characters, whether it's moving - or they are, and how it might be distorted by the environment.
This is the mood music outside your storyline, the music or sound that the characters are unaware of. If the lone character tiptoeing down to the basement after a cat could actually hear that menacing tone that you'd just put under their footsteps, they would be running back upstairs and out of the door!
You can use this in a few ways. Imagine you have two characters who have steadily fallen in love and are now, finally alone and confessing their feelings for one other. You can put some lovely, romantic theme under their scene to make the audience cry with joy for them (or quite possibly retch).
Alternatively, you could underscore it with an ominous tone. The audience will pick up the message that perhaps one of these characters is lying. Or perhaps one is about to die. Whatever, something will go terribly wrong...
Alternatively again, if you underscore it with the same music you used under those steps to the basement, the audience will be preparing for horror ahead.
Some producers use a certain theme for a location, rather than emotion. If the music comes in before the scene starts, then you can set the scene that way. Another possibility is to use recurring themes for characters, or even ideas. These are all called leitmotifs.
Imagine you start a scene with a beach, seagulls, rolling waves, the sound of children playing nearby.
And now mix in the music from Jaws.
Dun dun. Dun dun. Dun dun...
Immediately, many - if not most - of your audience will know what's coming. In the same way, with repetition, you can build your own show's sound vocabulary in your audience's heads.
How Much Music?
This is entirely down to personal taste - and also logistics. For Red Sands, apart from the theme, I used only stings and diegetic music. It was partly stylistic, as the noir-ish setup fitted with an Old Time Radio approach - but I was also grateful for that, as finding enough music to underscore 40 minute episodes would have been challenging.
Some mixers use music under every scene, or at least under the emotional part of it. Others prefer a more stripped-back approach. It's also worth thinking about how many other effects and background noises you want, so how rich the whole picture is going to be. It's worth experimenting a lot - and remembering to give yourself plenty of time to find the right music. You may need to loop it or stretch it slightly to fit it with the dialogue.
You need to find Creative Commons music if you are making a free production - and even then read the small print about how and where you can use the music. Some sites such as Kevin MacLeod's Incompetech or Jamendo offer some CC music with clear guidelines for use.
Otherwise, you can always approach composers - and in fact, I'd recommend that you do. I used many tracks from Newgrounds, where I contacted the composers directly, explained why I liked their particular tracks and how I would like to use them - and every one of them was more than happy to have their music used as long as they were fully mixed in and credited. Composers tend to like to hear their music being used and promoted, so it's a win-win situation.
All the best with using music and with finding that perfect track that fits your scene, character, location, emotion, idea, etc. etc.
MUSIC: FADE OUT