The website uses a free, automated tool that works with VOIP calling. You simply visit the home page, enter your phone number, and you'll get a call.
You can call international numbers with the service as well. In fact, you can also use the Ring My Cell Phone page to find international calling codes as there's a thorough list posted on the site.
This is a clever and simple site. It makes me think about what other reasons I might have to call my phone...! I think lost cell phones are the number one reason people use the site, but you could get creative with it, too. Maybe you're working on your laptop in a coffee shop, and someone won't stop bothering you, so you visit the website and make your phone ring and politely extricate yourself from the interaction with the other person by saying you have to take the call.
Well, now that you know the site exists, if you ever come upon a situation where you want your phone to ring, you can take advantage of the free service of ringmycellphone.com.