Yugi is the main character and the hero of Yu-Gi-Oh! He was given the Millenium Puzzle by his grandfather, Surogoku Mutou. Yugi then proceeded to solve and complete the Millenium Puzzle, thus accessing the hidden powers that awaited in it. Within the puzzle, Yugi gained a hidden spirit, an ancient spirit that comes out whenever Yugi plays a game. This is what is known in the Yu-Gi-Oh! series as Yami Yugi, or "Dark Yugi" in English. Yami Yugi is the only "good natured" spirit of the Millenium items and continually helps Yugi through all the tribulations set before him.
Starting with the Duelist Kingdom Story Arc, Pegasus J. Crawford, the creator of Duel Monsters, found out about Yami Yugi defeating the uncontested champion, Seto Kaiba. Pegasus knew Yugi had some kind of Millenium item, and in his quest to bring together all seven items, he lured Yugi into a major tournament held on an island named Duelist Kingdom. Pegasus lured Yugi, by first trapping him into a Shadow Game, in which Yugi lost due to the duel having a time limit. Since Yugi lost the "Shadow Game", Pegasus inflicted a "game penalty" to Yugi, thus stealing Surogoku's soul. This was the "bait" Pegasus needed to lure Yugi, as well as Bakura to the Duelist Kingdom, because Ryou Bakura was after Yugi's Millenium Puzzle as well.
With Yami Yugi taking over when the duels started, Yugi passed through most of his obstacles in the Duelist Kingdom, beating several challenging opponents. While doing this, he played with honor and skill, unfortunately, most of his opponents did not. He faced devastating opponents such as the sea duelist, Mako Tsunami, Weevil Underwood, Panik, Para and Dox, and Seto Kaiba, right before Pegasus' castle, where Kaiba unleashed one of Yu-Gi-Oh!'s most perilous and powerful monsters, the Blue Eyes Ultimate Dragon.
Once Yugi got in the castle and was named one of the Duelist Kingdom finalists along with Bandit Keith Howard, Mai Valentine, and Katsuya Joey. He faced Mai in the Duelist Kingdom semi-finals and won, unvailing his counter to the Blue Eyes White Dragon, the Black Luster Soldier, also known as the Black Luster Soldier. In the finals, he faced a suprising Joey, where they had an extremely impressive duel. Joey waited for Yami Yugi to play Summoned Skull, and with a quick combo, fused Summoned Skull with his own Red Eyes Black Dragon, creating Black Skull Dragon. Yami Yugi got past this ordeal though, taking advantage when Joey used his Time Wizard's effect to turn Baby Dragon into Thousand Dragon. Unfortunately, for Joey, he didn't know it would also turn Yugi's Dark Magician into Dark Sage. Yugi eventually beat Joey, let Joey take the claim to the prize money so he could help his sister, and Yugi went on to duel Pegasus.
Yugi and Pegasus laid high stakes on the line. Pegasus said he would free Seto Kaiba, Mokuba Kaiba, and Surogoku Mutou if Yugi won, but said Yugi would become entrapped and would lose the Millenium puzzle if he lost. After seeing and surviving Toon World and the Thousand Eyes Restrict, Yugi finished off Pegasus with the Magician of Black Chaos (Likely English Name: Magician of Dark Chaos).
Yugi later went on to help Kaiba fight the "Big 5" (the people who tried to take over KaibaCorp) and encounter Devlin in the Dungeon Dice Monsters. Currently, Yugi is participating in the Battle City tournament and wields the god card, Osiris, as well as Joey's Red Eyes Black Dragon (see the situation in later updates, and in Joey's bio, how he lost Red Eyes).
Yugi's Duelist Kingdom deck, or rather, Surogoku's deck has a Dark Magician Theme, with support from a ritual theme. Surogoku's deck is very ingenious at first, but when Yugi loses Exodia, and gives Joey his Time Wizard, it strictly becomes a basic Dark Magician Deck supported by ritual monsters. Yami Yugi, being the great duelist that he is, constructed a new deck for the Battle City Story Arc, and so far, it has worked to satisfaction, leading Yugi far into the tournament finals. While it still centers around the Dark Magician, Yugi has added a few counters to his new deck to the Blue Eyes White Dragon, such as the Buster Blader, and when Joey refused to take his Red Eyes back when Yugi won it back from a Rare Hunter, Yugi kept it in his deck. So now, with Red Eyes and Summoned Skull both in his deck, he can fuse them into Black Skull Dragon.