Use
GIMP. I can speak from experience as a long time low-tech Paint (and The Games Factory, oddly enough) user that it's fairly easy to get into; if you have an image from somewhere else and want to make part of it transparent in GIMP:
1) Start a new file or open the file you want to replace.
2) Paste.
3) On the layers dialog (Ctrl + L), press the new layer button in the lower left to make the pasted image into a layer.
4) Click on the "Background" layer, then the trash can to delete it.
5) On the toolbox, choose the magic wand.
6) Select an area you want to make transparent.
7) Hit the delete key.
8) Repeat steps 6 and 7 for all the areas to be transparent.
9) Save.
If you need any help, I'm new to this too, so feel free to ask me, but with the knowledge that I probably don't know nearly as much as some of the other guys here.