Yeah the issue you are having is thinking that it has all the commands you need when in reality you have to actually write them.
There are a few ways to alphabetize a list. I thought you could use the "sort" parameter for the listbox in the dialog event. If you want to switch back and forth you will have to take note when they click on the header as MPDreamz told you, then sort the list how you want it.
You would also need to provide the graphic if you want to have that arrow point up or down on the header like in MS applications. Then again, I dont think y ou can put an image on the header. If you can't, you can create your own sort button.