Its pretty simple, but you HAVE to have your amateur call first to use it. I am not sure what PC system you use, but there is a version for PC, Mac, Android, and iOS, I am not to sure about Linux.
Anyhow you download the software install it and during setup you have to confirm yourself. If I remember right there are several ways to do so. I remember doing something with registering my home phone number and Echolink called me with a code or something.. its been awhile…
after that your ready to go…
If you get to that step and if you have AIM or something I could walk you through the rest and we could have a QSO…
As far as how Echolink works… Their site explains how the technical parts work… echolink.org
It pretty much works by repeaters that a "linked" together via the internet. Some if not most of the linked repeater are ALSO "real" repeaters in the sense that HAMs that are within radio distance can use them with the traditional HAM radio.
So for example, I live in Columbus Ohio, I have a Friend that lives in Toledo Ohio (roughly 120miles North of me) obviously that is out of range for a 2m radio. I am able via Echolink to use my buddies Toledo linked repeater from my computer in Columbus. So I talk to him from my computer and he replies to me with his radio gear because he is near by the repeater.
Hope that makes sense. And honestly that is ONLY one example of what you can do with Echolink… it will do many other cool things too.