I presume you know how to place a trigger, and that you have saved your mission at least once.
Take your piece of music you want to use. It should be made into an Ogg Vorbis file, using programs like dbpoweramp or wavesurfer. If you go to the editing section of OFPEC, you should find a tutorial on placing music in a mission. It will also tell you where to get both programs I've mentioned. Read the tutorial, then read on.
Did you read it? Fine. You should have your piece of music in ogg Vorbis in a music folder in the folder of your mission and also declared in the description.ext file. Once you have done this, go into flashpoint and open your mission in the mission editor. place the trigger wherever you want, and place it's conditions and any extra activations you want to happen. Now click on the effects button on the bottom of the trigger editing screen. Go to the music area of the effects screen and scroll down all the available music. At the bottom of the scroller you should find the name which you named your piece of music in the description.ext file. Select it and exit the trigger. Start up the mission and see if it works.
If you need any more help, just post here. I'll be watching this thread.