"I have established that I need to use this url: https://api.stackexchange.com/2.1/users/1272330?order=desc&sort=reputation&site=stackoverflow ..."
That is the correct path to use, but the
sort query string parameters are unnecessary since you will always be receiving only one item in the response.
"... how to handle the response (or get one) from a script."
In both cases, the actual response will be in JSON format.
Instead of interacting directly with the API, I would highly recommend using one of the existing libraries / wrappers. I have written a library for PHP that is compatible with version 2.0 of the API: Stack.PHP. I wrote a brief tutorial describing the usage of the library.
jQuery.ajax() method of the jQuery library.
Edit: as requested, here is an example demonstrating how to fetch a user's reputation withs Stack.PHP:
$stackoverflow = API::Site('stackoverflow');
$user = $stackoverflow->Users(1272330)->Exec()->Fetch();
The example above will output the reputation of user #1272330 on Stack Overflow.