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This falls under the "obvious" category (like probably most of my posts), but as I had trouble finding it before, I figured I'd share this tip. To make a phone call from GMail, with the new Hangouts features, follow these steps:
First, sign into Hangouts. I used to keep my account signed out as I used Adium for IM, but I've switched to using Hangouts for all my IM conversations now. (Note, in the screen shot below, I'm using Firefox and an older account of mine, which accounts for lack of crap in my inbox ;)
After you sign in, click the Search button:
In the popup, notice it has a phone icon there, that's your first clue. But it may not be obvious how to dial. Just enter a number.
In case you're curious, I used sophisticated NSA-level methods to obfuscate the number in the screen shot. And that's it - just click the number and it will dial. A popup window for a new Hangout will launch and that's it. Obviously you get a dial pad (I use it a lot for Adobe's phone call meeting service) and you can mute yourself as well. You may want to check the settings to ensure it picks up your mic. My laptop has a mic, but I have an external one as well, and on a recent call it was using the wrong one.