Voldemort and Tom Riddle
Voldemort was once an orphan named Tom Riddle. He rose to power in the Wizarding World in the 1970's. His power was unmatched by any in history.
Attack on the Potters
Voldemort had learned of a prophecy that said a boy would be born that could destroy him. Voldemort, knowing Harry fit under the conditions set by the prophecy, set out to kill the boy. Lily Potter died protecting her son. The ancient magic of such a sacrifice protected Harry and nearly destroyed Voldemort. He could not be destroyed because he had split his soul into several pieces, giving him immortality. Harry also received a part of Voldemort's soul, making Harry another Horcrux, something Voldemort never knew.
Eleven Years Later
After Voldemort was thwarted by Lily's sacrifice, he was left as nothing but a mere whisper of what he once was. He fled to Albania, weak and with very little power. Luck was in his favor as he came across Professor Quirrell, a Hogwarts teacher, and was able to gain his assistance. Voldemort forced Quirrell to go after the Philospher's/Sorcerer's stone in order to regain more power. Harry had figured out that someone was going after the stone, and so the trio set off to stop whoever was responsible. Quirrell was unable to harm Harry because he could not touch him due to Lily's sacrifice. Harry thus stopped Voldemort from gaining strength from the stone.
The First Horcrux
Ginny Weasley unfortunately got hold of a diary that contained a shard of Voldemort's soul. Ginny conversed with the enchanted book and Voldemort took advantage of her and forced her to open the Chamber of Secrets. Harry confronted Voldemort in the Chamber who appeared to him as his sixteen year old self, known then as Tom Riddle. Tom ordered the monster of the Chamber, the Basilisk, to attack Harry. Harry managed to kill the Basilisk with the sword of Godric Gryffindor. He then destroyed the diary with a basilisk tooth, thus destroying a Horcrux. Harry would not learn what exactly the diary was for several years, however.
During Harry's third year, Harry uncovered the mystery concerning the identity of the man who betrayed his parents and handed them to Voldemort. Harry stopped Sirius Black and Remus Lupin from killing Peter Pettigrew who was the real traitor. But before they could hand him over to the Ministry, he escaped to search for his former master, Voldemort.
Through a set of mysterious circumstances, Harry became a participant in the Triwizard Tournament. Even though he was younger then his competitors, he did well and made it to the final task. Both he and Cedric Diggory, in a show of unity, reached for the prize at the end of the task and were immediately apparated to a graveyard. Peter Pettigrew was waiting for Harry and kills Cedric on Voldemort's orders. Using Harry's blood, Pettigrew used an old ritual to give Voldemort a new body. Voldemort then forced Harry into a duel. Harry attempts to disarm him just as Voldemort uses the Killing Curse. The wands react strangely as shadows of Voldemort's victims appear and distract him long enough for Harry to escape. Harry later learns this effect (called Priori Incantem) was caused by the fact that his and Voldemort's wand share the same core. Both wands have phoenix feathers from the same phoenix (Fawkes) in them.
Voldemort, now stopped from killing Harry twice, becomes fearful of him and wants to know how to destroy him. He begins a year long campaign to use the connection between he and Harry to full advantage. Harry begins to have dreams of a dark corridor that Voldemort seems to be fixated on. In a dream at the end of the school year, Harry saw Sirius captured by Voldemort. Believing it was a vision of the present, Harry went after Sirius, to the Department of Mysteries, only to find it was all a lie. Harry unfortunately fell right in to Voldemort's trap. He wanted the prophecy concerning himself and Harry, and only Harry could give it to him. In the ensuing battle against Voldemort and the Death Eaters, Sirius was killed. And less then a day later, Harry learned of the prophecy that bound him to Voldemort.
Although the Ministry now accepted his return, Voldemort did not take his war public. Harry's sixth year at Hogwarts was marked with disappearances and small disasters across London. Harry learned of the Horcruxes, though the information gained would not give him much to go on the following year. Dumbledore managed to destroy the second Horcrux; a ring that once belonged to Voldemort's grandfather. Meanwhile, Voldemort ordered Draco to kill Dumbledore. Draco managed to open a way for the Death Eaters to enter Hogwarts. He corned Dumbledore on the Astronomy Tower and disarmed him. Harry could only watch (under the protection of a spell and the invisibility cloak) as Snape was forced to kill Dumbledore when Draco could not.
Voldemort continued his silent campaign through the summer and continued his obsession with defeating Harry. He himself joined in the attack on Harry and his friends as they left Little Whinging. Using a borrowed wand he hoped to avoid the Priori Incantem effect. Harry's wand did magic of its own volition and the borrowed wand was destroyed. Voldemort was unable to pursue him any longer as Harry entered the protective charms of Tonks' parents house soon after.
Allowing his Death Eaters to control matters for awhile, Voldemort continued looking for a wand that would help him defeat Harry at last and make him unstoppable. This wand was called the Elder Wand. He managed to locate Gregovitch, a wandmaker who had the Elder Wand in his possession at one point. But it had been stolen by an unknown young man. While Voldemort was searching for the location of the wand, he left Nagini in Godric's Hollow as part of a trap. Just as he predicted, Harry (along with Hermione) came to Godric's Hollow in search of more clues. Nagini, under the disguise of Bathilda Bagshot's corpse, drew them to Bathilda's house in order to buy time for Voldemort to arrive. The two managed to escape just as Voldemort arrived. But, Voldemort found a photograph there of the very young man who had stolen the Elder Wand.
Voldemort set out to locate this young man and learned he was in fact Gellert Grindelwald, a dark wizard who had been defeated by Dumbledore nearly fifty years before. Voldemort began to figure out what had happened to the Elder Wand and realized that it had fallen into Dumbledore's possession after he dueled Grindelwald. Harry came to this same realization, but decided he was not meant to have it or stop Voldemort from getting it. His quest was still to focus on the Horcruxes. Harry watched, through their shared connection, as Voldemort made his way to Hogwarts once again and stole the wand from Dumbledore's grave.
The Last Battle
Voldemort returned to his headquarters and learned that the trio had stolen one of his Horcruxes from Bellatrix's vault at Gringotts. He finally realized that the secret of his Horcruxes had been compromised. As he carefully considered each Horcrux in his mind, he gave away the location of one more to Harry: Hogwarts. Voldemort quickly journeyed to the locations of all his Horcruxes only to find they were gone. He soon arrived at Hogwarts and prepared to attack. He delivered an ultimatum, telling the students and teachers that they need only hand over Harry and no harm would come to them. Of course, no one would turn Harry over (except some Slytherins) so the battle began anyway. Voldemort realized Nagini was now his last Horcrux and kept her close as he let his Death Eaters attack Hogwarts. Harry, meanwhile, managed to locate the fifth Horcrux, the lost diadem of Rowena Ravenclaw, and destroy it. Harry sought out Voldemort's location in his mind and the trio set out to kill Nagini in the Shrieking Shack. There they witnessed the murder of Severus Snape who passed on important information to Harry just before he died. Harry learned that there was actually one more Horcrux besides Nagini, and that was himself.
Voldemort was correct in assuming that Harry would come to him in an effort to stop the bloodshed. Finally, with the Elder Wand in his hand, Voldemort once again used the Killing Curse against Harry who did not even attempt to defend himself. Voldemort passed out briefly, and Harry apparently left the world of the living for the gateway between life and death. At this moment, Voldemort had failed to realize two very important things. First, he did not know that Harry had a bit of Voldemort's soul in him (a Horcrux) thus explaining the connection between them. Second, he did not realize that by using Harry's blood to form a new body he put Lily Potter's protection in himself. In other words, Voldemort and Harry were so connected in life that Voldemort could not actually kill Harry.
Thinking that he had won at last, Voldemort left the Forbidden Forest with his Death Eaters in tow as they headed to Hogwarts once more. Hagrid, meanwhile, carried Harry, whom everyone still thought was dead. However, the battle was far from over. Nagini was killed by Neville Longbottom, thus finally destroying all of Voldemort's Horcruxes. Harry went after Voldemort, surprising all the battle particpants, to face him in one more fight. Harry attempted to explain to Voldemort how he had failed with the Elder Wand because as it turned out, Harry was actually the Elder Wand's owner. Voldemort had again failed completely to understand things he did not think were important. He had falsely thought that Snape was the Elder Wand's master because he had killed Albus Dumbledore. But this supposed murder was pre-planned, which meant the ownership did not transfer to Snape. Instead, it had transferred to Draco Malfoy who had disarmed Dumbledore on the night of Albus' death. But Draco never actually touched the wand. While at Malfoy Manor, Harry disarmed and started to use Draco's wand. Thus, the ownership of the Elder Wand was Harry's all along.
As Voldemort once again tried to kill Harry but this time Harry used the disarming charm. The wand was unable to attack its true owner when Harry defended himself. Voldemort was destroyed at last.