How can I stop windows from rattling?
You need to figure out what exactly is rattling. Is the storm window rattling against the normal window, or is it parts of the storm window rattling against each other?

Without a picture to show exactly what's loose, my general suggestions are:


Tighten up any screws on the storm window--you can use some blue loctite on them if you want to prevent them from loosening up again. 
add foam weather stripping around the perimeter of the storm window where it contacts the normal window or house. This should take up the slack that allows it to rattle and make it more effective as well.
for any other gaps you can try wedging in some vinyl gasket weather stripping: