This is adeveloper-hosted app that demonstrates how to use the cross-domain library in SharePoint 2013  to read the items in an announcements list in the app web. The app deploys an announcements list to the app web, and the remote webpage displays the title and body of each announcement by using JavaScript and the client object model.

// The allAnnouncements variable is used by more than one 
//  function to retrieve and process the results.
var allAnnouncements;
var hostweburl;
var appweburl;

// Load the required SharePoint libraries
$(document).ready(function () {
    //Get the URI decoded URLs.
    hostweburl =
        decodeURIComponent(
            getQueryStringParameter("SPHostUrl")
    );
    appweburl =
        decodeURIComponent(
            getQueryStringParameter("SPAppWebUrl")
    );

    // resources are in URLs in the form:
    // web_url/_layouts/15/resource
    var scriptbase = hostweburl + "/_layouts/15/";

    // Load the js files and continue to the successHandler
    $.getScript(scriptbase + "SP.Runtime.js",
        function () {
            $.getScript(scriptbase + "SP.js",
                function () { $.getScript(scriptbase + "SP.RequestExecutor.js", execCrossDomainRequest); }
                );
        }
        );
});

// Function to prepare and issue the request to get
//  SharePoint data
function execCrossDomainRequest() {
    // context: The ClientContext object provides access to
    //      the web and lists objects.
    // factory: Initialize the factory object with the
    //      app web URL.
    var context = new SP.ClientContext(appweburl);
    var factory =
        new SP.ProxyWebRequestExecutorFactory(
            appweburl
        );
    context.set_webRequestExecutorFactory(factory);

    //Get the web and list objects
    //  and prepare the query
    var web = context.get_web();
    var list = web.get_lists().getByTitle("Announcements");
    var camlString =
        "<View><ViewFields>" +
            "<FieldRef Name='Title' />" +
            "<FieldRef Name='Body' />" +
        "</ViewFields></View>";

    var camlQuery = new SP.CamlQuery();
    camlQuery.set_viewXml(camlString);
    allAnnouncements = list.getItems(camlQuery);

    context.load(allAnnouncements, "Include(Title, Body)");

    //Execute the query with all the previous 
    //  options and parameters
    context.executeQueryAsync(
        successHandler, errorHandler
    );
}

// Function to handle the success event.
// Prints the data to the page.
function successHandler(data, req) {
    var announcementsHTML = "";
    var enumerator = allAnnouncements.getEnumerator();

    while (enumerator.moveNext()) {
        var announcement = enumerator.get_current();
        announcementsHTML = announcementsHTML +
            "<p><h1>" + announcement.get_item("Title") +
            "</h1>" + announcement.get_item("Body") +
            "</p><hr>";
    }

    document.getElementById("renderAnnouncements").innerHTML =
        announcementsHTML;
}

// Function to handle the error event.
// Prints the error message to the page.
function errorHandler(data, error, errorMessage) {
    document.getElementById("renderAnnouncements").innerText =
        "Could not complete cross-domain call: " +
        errorMessage;
}

// Function to retrieve a query string value.
// For production purposes you may want to use
//  a library to handle the query string.
function getQueryStringParameter(paramToRetrieve) {
    var params =
        document.URL.split("?")[1].split("&");
    var strParams = "";
    for (var i = 0; i < params.length; i = i + 1) {
        var singleParam = params[i].split("=");
        if (singleParam[0] == paramToRetrieve)
            return singleParam[1];
    }
}