The box should be big enough for the puppy to turn about in and even lie at full length, but no longer. The lid, or door, is required to keep the puppy from climbing out. Airline crates work well. Now, he might get caught the first night, but he won't the second. However, if the box is so large that he can relieve himself in one end and sleep in the other, he will do so.
Bedding can be plain newspaper laid out.
Remember that on the very first day it is important to start giving the puppy all his naps in the box. When the puppy awakens from his nap, you immediately lift him from his box and carry him outside to a spot which you previously selected. You must take him to this spot before and after play, always when he awakens from a nap, and always the first thing in the morning and last thing at night. Praise may include giving a small food treat. Within a week, you'll be well on your way to having him housebroken and going on command.