How to make a MultiMock Http Callout Test for Salesforce?

If I have an Apex function that is named authorize() that just gets a username, password, and session token, and another function called getURL('id#', 'key'), that takes an id# for the record as a string and a key for the image to return as a string as parameters. getURL calls the authorize function inside it in order to get the credentials for its callout. The authorize is a post request, and the getURL is a get request.

I am trying to figure out how to test both of these callouts just so I can make sure that getURL is returning the proper JSON as a response. It doesn't even have to be the URL yet which is its intention eventually. But I just need to test it to make sure these callouts are working and that I am getting a response back for the 75% code coverage that it needs.

I made a multiRequestMock class that looks like this:

    public class MultiRequestMock implements HttpCalloutMock {
        Map<String, HttpCalloutMock> requests;

        public MultiRequestMock(Map<String, HttpCalloutMock> requests) {
            this.requests = requests;
        }

        public HTTPResponse respond(HTTPRequest req) {
            HttpCalloutMock mock = requests.get(req.getEndpoint());
            if (mock != null) {
                return mock.respond(req);
            } else {
                throw new MyCustomException('HTTP callout not supported for test methods');
            }
        }

        public void addRequestMock(String url, HttpCalloutMock mock) {
            requests.put(url, mock);
        }
    }

I then began to write a calloutTest.cls file but wasn't sure how to use this mock class in order to test my original functions. Any clarity or assistance on this would be helpful Thank you.