We bought a dual processor G5 ~ 6-9 months ago. It's a nice machine. She also has a 667 MHz 15" Ti Powerbook.

Drool, envy etc.

I've set up accounts for both of us on the G5 but haven't really done anything complicated with them. The things I need to understand better are: 1) What's really happening when I install new software? What's going on with these Disk Images and the Drag-And-Drop Installation? Where should new software be put? 2) How do I adjust the file permissions so that she and I can each modify files or use programs without dragging them to a shared folder?

1) Disk images are like fancy Zip archives. You put software wherever you like. I dump mine in /Applications, but if it's just something one user uses, ~Applications is fine.

2) You don't. Welcome to UNIX :)