Answer:
I recently had to go to the post office to pick up two postage due. One was 5x5 and one was 6 1/2 x 6 1/2. Each one had a normal 44 cent stamp on it. I had to pay 20 cents more for the 5x5 and I had to pay 44 cents more for the larger one.
The rates are posted on the USPS web site. Square envelopes are charged a "non machinable surcharge" in addition to regular postage. That surcharge is 20 cents for any piece of first class mail as of March 2012. The non machinable criteria are outlined in the "Domestic Mailing Manual" in the "Physical standards" section. Letters need to have an aspect ratio between 1.3 and 2.5 to be considered machinable. The aspect ratio is the width divided by the height; square envelopes have an aspect ratio of 1, which is less than minimum 1.3 required.