With Facebook's recent announcement with Skype, they've now enabled video calling within FB's chat window.
So, if you're installing it the first time, you'll need to have to install a plugin. Of course, your computer should have a webcam attached or built-in. You can still install it, but you'll only be able to speak and you'll be able to see the other party if they have a webcam.
Before you go to the link to download the plugin... finish reading this step-by-step before you start installing. I have a tip further down.
So go here to get the plugin - https://www.facebook.com/videocalling
After you've done that you can call any of your chat buddies. Your friends would not need to install (like you just did) the plugin. All you have to do is click on the "video calling icon" (grayed-out - see the chat image below).
Your friend will get a pop-up asking to install/setup video calling. Once that is done, you can start using video calling.
Tip: If you know of someone who has already setup video calling, just ask that person to call you, and a pop-up will appear at your end. Just click setup and the plugin will be installed.
What I like is that you don't have to setup a Skype account. Easy and fast.