How To Update Selection List Contents From A Server Database Based Upon User Data Entry

I am trying to create a web page in which the contents of one selection list
depends upon which element in another selection list is chosen, but where
the information to populate the first selection list comves from an SQL
database on the web server.

There are a couple of these situations in my application but, for example,
the first list might be a list of counties, and the second list a list of
states/provinces. Obviously the names of counties depend upon which
state/province is chosen, but there are too many possibilities to be able to
embed them within the web page itself. So when the user selects a
state/province I need to go to the server to ask for the list of counties.

I have seen a number of posts that sort of address this issue. For example
it is suggested to use <script src="a URL"/> to ask the server side code to
send up data of type "text/javascript". However the examples do not seem to
address how the server side code would know which state/province the user
had selected.

If there is a web site that addresses this sort of thing, I would appreciate
any pointers.