public with sharing class MyContinuationController {
    // Unique label that identifies the continuation
    public String continuationToken;

    // Result of the long-running operation
    public String result {get;set;}

    // Method that starts the continuation
    @AuraEnabled
    public Object getstartRequest() {
        // Create continuation with a timeout
        Continuation con = new Continuation(40);
        con.continuationMethod = 'processResponse';

        // Create callout request
        HttpRequest req = new HttpRequest();
        req.setMethod('GET');
        req.setEndpoint('http://long-running-service.com');

        // Add callout request to continuation
        this.continuationToken = con.addHttpRequest(req);

        return con;
    }

    // Callback method that processes the callout response
    public Object processResponse() {
        // Get the response by using the unique label
        HttpResponse response = Continuation.getResponse(this.continuationToken);

        // Set the result variable that's displayed on the Visualforce page
        this.result = response.getBody();

        return null;
    }
}