Turbo Exodia is designed to get all of the parts of Exodia into your hand as fast as possible. On average, from the games that I have played with it, you should have every part of Exodia in your hand by the 5th turn.
The whole deck is about combos. These combos come with results in two forms: Getting the cards you want in a position where you can use them or getting cards out of the deck so that you will draw other cards that you would rather be drawing.
The best combo in this deck, when it works out, is to use Penguin Soldier with Magical Silk Hats. You take two Magic or Trap cards from your deck(preferably Distressing Choice and Reserves) and use them as the "fake hats." With a bit of luck, your opponent will attack the Penguin Soldier, and you can use it's flip effect to return the two "fake hats" to your hand, where they will be ready for use next turn. If the cards die, instead, at least they are in your discard pile, meaning that a Saint Magician or a Dark Mask can easily retrieve them, and your odds of drawing these two monsters are far greater than your odds of drawing the aforementioned magic and trap cards.
The second combo is to have a Reserves and Distressing Choice. Use Distressing Choice, and choose all of the arms and legs of Exodia. Your fifth card should be the last Reserves. If your opponent puts all 4 body parts in the discard pile, you can use both Reserves to get them all back. If your opponent puts a body part in your hand, you still only need one Reserves to get them all back. From here, you only need the head, and that means either drawing the actual head, one of the two Critters, or the Black Forest Witch. This combo brings you very close to victory.
Additionally, remember that the graveyard is a safe place for your Exodia pieces. It's okay to discard them, and it's okay to leave them there until you are ready to win. Just beware of cards that remove other cards from the game. Also, and this may seem obvious to some, it is often a good idea to attack your opponent's strong monsters to kill your own Critter and Witch. If you're close to winning, don't worry about the damage, because you can't always trust that your opponent will attack.
If something bad happens and you can't win, use Fiber Pod. It's there as a reset button to give you a second chance. Also, Kuribos and Messenger of Peace are mainly there to protect from the infamous Devil Franken Deck, but of course they are useful against any other damage-dealing deck as well.
If you can, avoid discarding the head of Exodia. It can't be retrieved through Reserves, which means you need to bring it back to life(which means in play) and then activate a Penguin Soldier to get it back to your hand. It's very troublesome, so you will want to avoid it if possible.
If you want to defeat this deck, use cards that negate flip effects and traps.
