Okay, I'll say the plot...might contain spoilers
The story takes place in a region called Amestris (Based on Germany), 1910. In this world, there is a science that transforms one form of matter into another. Imagine a pile of paper being transformed into a cardboard box in a blink of an eye. This science is called Alchemy. It's the science of being able to turn one form of matter into another. However, sicne it is a science, one must present an equal value in order to satisfy the rules of this science.
The Heroes of the anime/manga are the brothers, Edward and Alphonse Elric. Both are the sons of a famed alchemists, Hohemheim Elric. Ed and Al (their nicknames) didn't really get to see their father since he goes away for the military. Ed and Al just grew up with their mother instead. Soon, they begin to learn alchemy by themselves through reading books. Later, the boys can even perform simple alchemy. However, one fateful day, their own mother died. They were left with no family. The brothers soon began to think of reviving their mother through alchemy. However, they know that this act is forbidden since no one has accomplished it yet. The boys do it anyway. They "voluntered" themselves in order to become apprentices to an alchemist living in Dublith. After they learned all what they can about alchemy, they attempted to perform alchemy. While they were performing this forbidden act, something went wrong. They soon realized that they were missing something in their transmution. Before Ed could realize it, Al was being dragged towards "the other side." Before he could reach out for him, his leg was missing...
When Al woke up, he found himself transumted to an armor. He found Ed, bloody and missing an arm and a leg. He rushed him to their friend's house where he was confined to a bed. During the night, a state alchemist arrived after recieving a letter from the brothers. He invited Ed to come to Central City and become a state alchemist. The next day, when the man was gone, Ed wanted to become a state alchemist because of what he heard. He heard that State Alchemists have access to libraries where other kinds of alchemy is involved. He asked his friend's grandmother to replace his missing limbs with mechanical ones - automail. Edward soon recovers and with his brother, they head off to Central City. Later in Central, they discovered the powers of the "Philosopher Stone"
Meh...I'll stop...