A puppy that is bored will look for his own entertainment. What he chooses to do is rarely what you would want. Chewing, digging and other destructive behavior is typically the result of a puppy having lots of energy and no means of expending it. Deal with boredom issues as soon as you notice them, because the behavior he develops as a way to relieve boredom can quickly become a habit difficult to change even after you address the issue.
Provide adequate physical activity. Even if your puppy has access to a fenced yard, he will probably not exercise himself enough to truly wear himself out. Throw a ball, take him for regular walks or simply run around in the yard with him. Anything that gets him moving will work off excess energy and make him more content to flop down and nap once he's back inside.
Teach your puppy basic commands and simple tricks. While you shouldn't expect a young puppy to learn advanced skills, such as walking beside you off-leash or sitting in one spot for an extended period of time, he can learn to walk calmly on a leash, come when called and fetch a toy. Teaching him these skills will train him to listen to you, work off excess energy and keep his mind busy, which will alleviate boredom.
Play with toys that keep his mind busy. There are many puzzle-type toys available that can help fight boredom. You typically place treats in these toys, and your puppy must work the treats loose. These toys make excellent playthings for when your pup is left alone.
Cycle through his toys rather than providing them all at one time. If your puppy has access to all of his toys at one time, he will probably get bored with them quickly. Instead, keep two or three toys out, and the rest put away. When he seems to loose interest in a particular toy, put it up for a while, and get a different toy out.
Interject short bursts of playtime throughout the day. Play sessions don't have to be long to be beneficial. Five- or 10-minute sessions interspersed throughout the day are effective at keeping puppies from developing bad habits associated with being bored.