1. Login to your Live Agent admin panel
You can use "Login to Admin panel" button directly from your Magento.
If you do not see it, then fill and save form "Account Settings" from LiveAgent menu in your Magento. If connection will be sufficient, you'll see "Login" button instantly.
Now in your LiveAgnet panel go
Click edit on button, you want to be visible on your page
You'll see your button options. Now scroll down to Integration section, and copy this code to Button code section in your Magento.
Now hit "Save" button and you are all set! Refresh your Magento store page (from customer point of view) and you'll see your button instantly.
NOTE: Be sure you use the latest LiveAgent plugin for Magento.