I'm 15 and have had my period for about 3 years. During this time, I've discovered a few helpful ways to ease the pain caused by this monthly 'gift'.
(These work for me, but everyone is different):
Bananas- Bananas are high in potassium, which can ease muscle contractions and relax the body.
The Fetal Position- this usually takes a few minutes to work
Pressure- putting pressure directly on the pain areas helps a lot. When the pain is in my lower back, I use the tips of my fingers to try and roll it away. When it's in my stomach and hip region, I use my knuckles.
Heat- heating pads, warm towels, etc.
Exercise- it may sound strange, but it works. Stretching or yoga works best. It may cause some severe momentary pain, but it helps to keep the cramps from returning.
Breathing deeply- hyperventilating and short, ragged breathing causes muscles to contract and makes cramps worse. Take slow, calm breaths and try to steady your heartbeat.
Staying still- laying in one position for a period of time helps ease the pain
Here are some things that can cause cramps (best to avoid!):
Dairy- especially ice cream. The lactose in dairy helps strengthen muscles that stimulate contractions (good for sex, bad for cramps).
Making loud noises- talking loudly and yelling contract your abs, which for some makes cramps better, but makes them worse for me.
Tampons- these make the muscles work harder to compensate for the intrusion of an object. Try pads.
Alcohol- alcohol may relax some muscles, but it will ultimately lead to the feeling of a hangover in your uterus.
Tight jeans- it may sound cliche, but wearing tightly fitting pants constricts the body and makes the muscles rub together and behave abnormally.
Bad posture- slouching opens the back muscles up for the full frontal hit of cramps.
High body fat- for some reason, the healthier weight you are, the less agonizing the cramps. Eating healthy and stretching for at least 10 minutes a day helps alleviate tension that can cause cramps.
Medicine's can be an easy way to temporarily alleviate cramps, but not in the long run. I'm vegan and straight edge, so I can't give a personal opinion on the effectiveness of pills, but I have friends that use them (Tylenol, Advil, Midol, Ibuprofen, etc etc) and say that they aren't very helpful.
Hope this helps you!