It's sort of trial and error at this age because you can't talk or reason with them, they're just little bundles (smile). You want to do what is best for him, and helping him form good sleep habits is a start. He doesn't yet understand what's best for him, and will cry if he doesn't get what he wants. Your goal is to help him learn to sleep and fall asleep alone. There are a few different things you can try, make sure the one you choose is something you're comfortable with, and make sure that once you start an approach, that you stick to it.
For starters, don't let him sleep too much during the day, and hour or so twice a day right now is good, but if you let him get all of his sleep during the day, he's going to be a little night owl. Help him learn to settle down and comfort himself. I don't like to let them "cry it out" per say, but don't jump at his first whimper either.
Wait a few minutes to see if he's really upset and awake, and then go in and reassure and comfort him without removing him from the crib. Instead, soothe and pat him with your hand and talk quietly to him. Do not turn on the lights or make excessive noise. At first, go every few minutes, but eventually call to him from outside of the room.
It's a good idea to create a calm, supportive bedtime ritual and environment, including a bedtime story, a special night light or lamp, princess sheets, a bath, a favorite teddy or bunny, prayers, songs and so on.
If you stick to it, and be patient, eventually he will fall into the routine and start sleeping longer.
Other options may include talking to the pediatrician about the teething. Making sure he isn't waking up because he's hungry, he may need more food. If he's not eating cereal yet, it may be time to start.
There's a great book you may want to look into called On Becoming Babywise.
Thanks for that additional info. When she waits outside of his room (or just inside the door) , she can talk to him and try to sooth him without picking him up. If she thinks it's teething, she may want to use orajel or something similar in addition to the Tylenol. Also, she may want to feed him cereal before bedtime as well as feeding him.
Understand that anything she tries, it may take up to 2-3 weeks to see a difference. So you can't try something for a few days and then assume it's not working. Thats why you need lots of patience.
It sounds like you guys are doing everything right, so it may be hunger or it may be teething. You're right, getting exhausted isn't good, and can cause a lot of irritation. Hopefully they can take turns. If she is a stay at home mom, she should try to nap when the baby naps. Try the cereal at bedtime and if you want to come back in a week and let me know how it's going that would be great.