Start by making a new image and choose transparent as background.
That will give you with a checkerboard-looking pic. Which is the default look of transparent pictures.
Just so that you can see the effect,
make a new raster layer and fill it with black.
Then create another raster layer and fill it with some other color.
Now take a look at this pic:

The sliders (marked 100) is the level of transparency for the different layers. Just adjust each layer as you please.
When you're done, save as png. And you should have a transparent or semi-transparent pic.
Hope I made it somewhat understandable..
And here's a layer-tut if you need it:
http://www.psphelp.com/v7_layers.php