Personally I would start with a sample that you like, maybe something that sounds like the beep. I'm a linux user, so I'd open up Ardour 3 (which is also on Macs, and is totally awesome) and then for each layer in the sound, have a new track.
I'd put a delay on the beep, so it sounds like it's decaying for the first sample. I'd add an explosion sample, low pass it and then window it. Then add a few other bits and pieces in to fill out the sound. I've had great success using softsynths like ZynAddSubFX, which, although the learning curve is steep, you can create anything you like.
You can either build it up with wave forms and place them where you want to, or you can actually sequence them together using midi, being driven by a softsynth. The sample is also heavily compressed.
This is not the be all and the end all, it's just a pointer to where to start. Break up the sound you want, and add more tracks until you get it. If Ardour scares you, start with Audacity and get all the LADSPA/DSSI plugins.
Basically start somewhere. You don't build a building without stages and sections.