In a perfect world, you could get through life without having upstairs neighbors, but this world isn't perfect. While buildings all carry noise differently, stomping from an upstairs neighbor can be stressful, keep you from sleep and make you hate being home. There are many ways to dealing with stomping or other noise from an upstairs neighbor without hitting your ceiling with a broomstick and yelling. A lot of times people don't realize how much noise they are making.
Introduce yourself to your upstairs neighbor and ask for his name. Explain that you live below him and that you are having trouble dealing with the noise from his stomping or other noise-making. Stay calm and simply ask him to try to keep the noise down during the hours you are asleep.
Talk to your building's landlord or super if the upstairs neighbor continues to make noise despite your request. You may first try taping a note to her door explaining the noise is still bothersome. In many buildings, landlords will talk to the neighbor and handle the problem for you, but that is not always the case.
Wear earplugs or headphones if the noise is too loud for you to sleep. You can also try soundproofing your apartment with egg cartons or professional soundproofing padding if you really can't stand it.
Take legal action if your landlord does nothing. While you may not get any money from the person, you can file a civil complaint to show the upstairs neighbor you are serious and that he is hindering your life. Especially if you have lived in the place longer than the neighbor, you may be entitled to have the person evicted or otherwise penalized for the noise.
Move out of your apartment if the upstairs neighbor doesn't stop making the noise and legal action is not an option. If you are in a lease and the landlord does nothing about the noise problem, you are legally justified to break the lease due to unlivable conditions. If your landlord or lessor disagrees, an attorney can help you.