Not to worry, I have a purple rug (handy, right?). The only problem is that it's a remnant so the edges aren't finished, it looks like a crazy frayed mess.
On to the internet I go....I'm envisioning myself hand binding a rug with a curved needle and embroidery floss for the next 5 years.... GAK! After about 11 seconds of searching I find this awesome product from a company called Bond Products, Instabind. For well under $100.00 I get a 54' roll of instant rug binding! The website is really nice, there are videos of how to use the binding, clear pictures of the colors and styles available, prices right up front and super zippy shipping!
Once the tape is all on, you go back around with your hot glue gun, run a little bead along the edge and press the carpet down firmly. When you get to the end, you overlap slightly and glue the ends together.
Now back to painting the livingroom!