Click on the Messenger you want to embed and copy your code snippet.
Paste it in the header or footer of the site of which you're installing the messenger.
There are many website platforms, but here is an example on how to embed header/footer code in a Wordpress website.
Login to your Wordpress admin.
Install this plugin. (There are many plugins that offer this functionality.)
After installing and activating, inside the Wordpress dashboard navigate to Settings > Header and Footer.
Under Head and footer tab paste your code snippet you copied from above. Be sure to save and publish your site.