Hi,
The easiest way will be WITH reloading the page.
Without:
1) If you have limited set of data, you can load it all at once during page creation. Then it's pretty much javascript - you'll have to re-create drop-down lists on-the-fly, which means you have to use onChange event for all dropdowns.
2) If your lists are long - very long, there is other way
a) create iframe on the page
b) user selects the entry from first list => content of iframe is changed by onChange event (e.g. iframe location is set to the script (php-script) that fetches the data for second drop-down. Once data is fetched, the javascript in main frame re-creates second dropdown.
I don't like either one of this ways 🙂