Step 1: You Have an Empty Box . . .
Step 2: Draw All of the Legs
Step 3: Cut the Waste Areas From the Flaps.
It is easy to "overshoot" your cut and have your knife turn on you. Also, the double-thickness cardboard used for computer cartons will dull a box cutter very fast. Snap off new knife edges often, to have a sharp cutting edge.
Step 4: Make the Reindeer's Head
Do full-cuts through parts of the drawn lines, but only cut the top layer of the cardboard in the middle of the lines (It will make sense when you see the picture).
Remove the waste areas to make two flaps on the sides of the head.
Step 5: Attach the Head to the Body
Step 6: Make the Antlers
Take a look at some reindeer (or pictures of them) to see what the antlers are SUPPOSED to look like.
Step 7: Attach the Antlers
Step 8: You're Done! Merry Christmas!
With a little extra work, you can make a more 3-dimensional head, cut out nostrils and eyes, add some ears, etc.
You can also attach a red LED to the end of the nose, if you're really making a special reindeer.