Most live chat tools are encapsulated in a Javascript snippet to add to your site.

WordPress, for example, may provide a plugin + if you look at the plugin code, usually the code simply injects the Javascript snippet.

This said, all you really require... choose how you'd like the live chat icon/window/widget to display + likely the live chat provider will have a library of code to display their live chat window in different ways.

If you are adding a live chat feature to a WordPress site, search the "live chat" tag in the WordPress.org plugin repository to find top rated plugins. Some popular choices are: Intercom, Snap Engage, Tawk.To, Olark, and WP Live Chat. If you are already using a helpdesk like Zendesk or Help Scout those services also have chat tools and extensions. Either the plugin or a javascript snippet (as mentioned above) will add the feature to your website. The services mentioned above have great support documentation to make that process pretty straightforward. You would still want to run Google Analytics on your site for visitor data and goal tracking.

As per my experience we have been using Zendesk and didn't face any issues either with technicalities or support.