Install the Echolink software on your computer (for Linux, there's a client call Qtel, available in standard package repositories), connect your computer to the internet, register with the Echolink web site and confirm your call, set up the software with your call and Echolink password.
Now, when you start the software (at least on Qtel, I presume this works much the same on the Windows client) you'll get a long list of on-air repeaters and ongoing "conferences" that you can select and connect to. Connect to a repeater, and you can send and receive through it, using your computer (I'd recommend a headset/microphone combination, commonly sold for internet phone service such as Skype), just as if you were connected to the repeater with a hand-held, mobile, or base rig.
For instance, I live in North Carolina, but I lived in Seattle for twenty years before moving here. I found a couple Seattle repeaters on the list in Qtel; I could connect to one of those and call over the air in Seattle, hopefully make QSOs with Seattle operators, as if I were within reach of the repeater I'm using -- but my connection goes via Internet from here to Seattle, and over the air only from the repeater to the Seattle operator who hears or answers my call.
This has nothing to do with what radio you have; you aren't even using a radio (you need a license, though, because you're transmitting at the other end of the Echolink connection).