Custom template with data based on URL

I’m surprised how little information is out there to accomplish what I want to accomplish. My specific use is front-end user profiles with clean URLs, but the same concept could apply to lots of use cases.

I am looking for a full end-to-end explanation of how to accomplish the following:

If a user goes to http://www.mywebsite.com/users/username it should display a profile (based on my custom template) for the user with username “username”.

I’m assuming the way this should work is I have a custom template file that reads in the URL, parses it and retrieves user data based on the username provided in the URL.

How do I get these URLs to trigger this custom template, or maybe I should say, how do I get the custom template to load based on the URL itself? If i want to change that slug “users” to something else, even something like http://www.mywebsite.com/group/fans/username, how do I do that?

Can someone provide a full explanation on how to do this? Thanks very much.