I apologize for the crude blocking on the box—it's actually my husband's Christmas gift and I didn't want him to see it. Also, for the record: no one in Japan would ever wrap in old newspaper.
Start with your gift placed at an angle—you'll be wrapping corner-to-corner. (This method can be applied to any object of any shape, but it's easiest to understand with a box.) For ease of discussion, I'm going to label the corners north, south, east and west.
Bring the south corner over the top.
Then pinch the top of the paper on the west side, as if making hospital corners on a bedsheet. Crease it sharply and fold it onto the top of the box.
The camera is now looking on from the southwest side. Push the paper on the west side in, and bring the west corner over the top. You can tape it down at this point if you like.
Repeat with the east side of the paper.
At this point, you have a sort of envelope with the flap open, and this is the one place it gets a little tricky: you are going to fold in both sides at once. I hope the photo is self-explanatory, but basically you push both sides inward as you simultaneously lift the north corner up and over the top. Crease the folds against the side of the box and tape. (Once you get the hang of things, this will be the only piece of tape you need.)
And that's it! Gift wrapping that takes 60 seconds and one piece of tape—what's not to like? :)