The following steps are how to create a Facebook App to allow the facebook messenger chat to appear in the bottom right of your website.
Step 1: Create an app here.
Step 2: Copy and paste the code below into the end of body and replace the App ID and Page_ID. You can find your App ID at the top of your app and you can find your page id on your facebook page, specifically on your about page.
Step 3: Configure the settings in the developer account and Facebook page settings area.