This is one way to pack your puzzle for shipping without using a larger box. This will help keep your puzzle safe while being shipped and will keep your cost down.
You will need some supplies. Scissors, tape measure (or ruler), scotch tape, 2" packing tape, a kitchen scale (or mail scale) and some brown paper. (grocery bags work well)
It is important that you put your puzzle pieces into a zipper baggie. If for any reason, your package is damaged, you don't want the puzzle pieces escaping and getting lost. By placing the pieces in a zipper baggie, you can be sure the puzzle will make it to the destination with all the pieces intact. If something does get damaged, the post office will normally repack your box but if pieces are lost before that you are out of luck. So use zipper baggies.
Next you want to use scotch tape to seal at least 2 opposite edges of the puzzle box. Doing all four sides doesn't hurt and could add some protection. But tape at least 2 sides. You only need about an inch of tape on each side.
Now, place your box on the brown paper and cut the paper so there is at least one inch of overlap around the middle. You will want the flap on the ends to go just past the half way point. You don't want it to go all the way to the other side of the box because it will cause issues when you put the packing tape on. The final seam should be just past the half way point. Here you can see what I am talking about.
Everywhere the paper overlaps, place a small amount of scotch tape. A half inch or so will do the trick. This is only temporary and will be covered by the packing tape. It is just a lot easier to work with the scotch tape while doing the basic wrapping.
In many cases, your puzzle box will be much smaller than the paper you have. The easiest way to trim it off is to make sure one end has the proper overhang (see above) then move the box slightly off the end of the table and match the overhang on the long side. It is easy to just snip into the paper and work your way around. The cut doesn't need to be pretty. Again shoot for an overhang just slightly more than half way across the puzzle box.
Now fold the two ends in like you are wrapping a gift. Start by folding the short ends in, then fold the side with the seam down and the side without the seam up and put a bit of scotch tape in place to hold things for a moment.
Now you are ready for the packing tape. Notice that the puzzle box is about 2 inches wide and your packing tape should be about that same size (just a bit smaller). If you have a thicker puzzle box, you may need two bits of tape but only if it is a good deal bigger. The goal is to protect the flap and the corners. So your tape should extend about 1 or 2 inches past the side you are taping and go all the way across the seam.
You can use a piece of packing tape to go across the bottom of the box and to seal that seam as well. You can do the bottom before or after doing the two ends. It makes little difference.
You are now done with the basic packing job. It is time to measure and weigh the box. Measure all three directions to get the length, width and height of the package. A standard Buffalo puzzle is 8 inches by 8 inches by 2 inches. You will also need to weigh the package. This is easiest with a cheap digital kitchen scale.
You are ready to purchase your shipping label. There are several places to buy labels from. I like to use PirateShip.com but you can use any shipper you like. I have a list of the main shippers in the USA.
After you have your label, simply use the packing tape to fix it to the package. I like to put several strips of tape over the label to make sure it is protected from rain.