A couple of ways:
1) put the music track down first and edit your visuals to the music, so that shots might change with every other beat for tight synchronization.
2) Edit your visuals, dialogue and sound effects, then put the music in last.
To do this, you need an editing program. Use the first 2 or 3 tracks for cutting dialogue or the sound that is actually attached to your video images.
If you have a lot of sound effects - background ambience will take up a track or two and you may have telephone rings, gunshots, tires squeeling, etc. Plan on 2 or 3 tracks for effects.
Lastly, you will put music on a couple of tracks. For ease of understanding, lets say 3 tracks. This means, you will have 9 total tracks - 3 stereo tracks for dialogue, 3 stereo tracks for sound effects and 3 stereo tracks for music. Multiple tracks will allow you to fade/overlay music tracks on top of each other for transitions.
Ultimately, if you edit sound for features, this kind of track separaton will allow you to turn - say the dialogue - "off." A foreign company can now dub your movie, yet have all the sound effects, ambience and music. These are called M & E tracks and most distributors require them.
Okay, so we're talking about a short with two pieces of music. The editing program should allow you to add as many tracks as you need. So you have a couple of tracks for dialogue and you can put music on track #3. As long as the musical pieces don't need to overlap, you can use the one track.
Your editing program will probably have some sort of mixer or volume control, so you can make the music track softer than the dialogue - waaaay softer, while talking. Bring it up for the action/suspense moments. In Premiere, I add keyframes or handles that you can raise or lower on any of the tracks. If you put one handle all the way down, followed a couple seconds later by a second handle at normal level, this will create a fade in. Do the opposite for fade out. Or add a couple of handles under the dialogue and pull them down so you can hear the words clearly.
When I make music on a keyboard, I make a wave file out of the song, throw it on a jump drive and put it in my main computer for use with the editing program. You can also record into your camera and CAPTURE the audio through your firewire, USB, etc. - same way you captured the video.