Usually it's fairly simple: You receive a snippet of code to plug into your website along with detailed instructions from your tool provider for yourself or your IT department to follow.
Where some of the live chat tools differ from each other is how you make changes to your setup or the appearance of your chat client. With some tools you have to re-insert the code, while others will dynamically change, which is a lot more convenient.
Installing a live chat tool is really simple and literally only takes a few minutes. Just take a look at this example: