These are the cards and how to get them in Yugioh: Legacy of the duelist, in order to win on your first turn:

Monsters:

1x Left arm of the forbidden one. (Grandpa)
1x Right arm of the forbidden one. (Grandpa)
1x Left leg of the forbidden one. (Grandpa)
1x Right leg of the forbidden one. (Grandpa)
1x Exodia the forbidden one. (Grandpa)
3x Royal magical library. (Yami)
3x Broww, huntsman of dark world. (Bastion) (GX)

Spell cards:

3x Broken bamboo sword. (Quinton) (Zexal)
3x Golden bamboo sword. (Quinton) (Zexal)
3x Dark world dealings. (Bastion) (GX)
3x Graceful charity. (Grandpa)
3x One day of peace. (Quinton) (Zexal)
3x Pot of duality. (Grandpa)
3x Pot of greed. (Grandpa)
2x Spell power grasp. (Yami)
2x Toon table of contents. (Seto Kaiba)
1x Toon world. (Seto Kaiba)
3x Upstart goblin. (Grandpa)

No trap cards.

Effect of each card:

Broken bamboo sword:
'The equipped monster gains 0 ATK'

Dark world dealings:
'Each player draws one card, then each player discards one card'

Golden bamboo sword:
'Activate only if you control a 'bamboo sword' equip spell card. Draw 2 cards'

Graceful charity:
'Draw 3 cards, then discard 2 cards'

One day of peace:
'Each player draws 1 card, and neither player takes damage until the end of your opponents next turn'

Pot of duality:
'Excavate the top 3 cards of your deck, add 1 of them to your hand, also, after that, shuffle the rest back into your deck. You can only activate 1 "Pot of duality" per turn. You cannot special summon during the turn you activate this card.'

Pot of greed:
'Draw 2 cards'

Spell power grasp:
'Target 1 face-up card on the field that you can place a Spell Counter on; place 1 Spell Counter on that target, then you can add 1 "Spell power grasp" from your deck to your hand. You can only activate 1 "Spell power grasp" per turn.'

Toon table of contents:
'Add 1 "Toon" card or "Manga ryu-ran" from your Deck to your hand.'

Toon world:
'Activate this card by paying 1000 LP'

Upstart goblin:
'Draw one card, then your opponent gains 1000 lifepoints'

Broww, huntsman of dark world:
'If this card is discarded to the Graveyard by a card effect: Draw 1 card, plus another card if this card was discarded from your hand to your Graveyard by an opponent's card effect'

Royal magical library:
'Each time a Spell Card is activated, place 1 Spell Counter on this card when that Spell Card resolves (max. 3). You can remove 3 Spell Counters from this card; draw 1 card.

Exodia the forbidden one:
'If you have "Right Leg of the Forbidden One", "Left Leg of the Forbidden One", "Right Arm of the Forbidden One" and "Left Arm of the Forbidden One" in addition to this card in your hand, you win the Duel.'

Cards without effects:
-Right leg of the forbidden one
-Left leg of the forbidden one
-Right arm of the forbidden one
-Left arm of the forbidden one

This is a guide explaining how to use each and every card in the exodia deck effectively in order to win on your first turn.

Broken bamboo sword:
Equip to a royal magical library when you have one available.

Dark world dealings:
Discard a spare card that has no use to you, or is "Broww, huntsman of dark world".
These include: "Toon world" and "Broken bamboo sword" (assuming Bbs is already equipped to a royal magical libary) And these cards if you've already used one this turn: "Royal magical library", "Pot of duality", "Spell power grasp". Preferably better to use when you have these spare cards available. Use other cards in your hand that simply gain cards first to make use of your discarding.

Golden bamboo sword:
Equip "Broken bamboo sword" to a monster first. (Preferably "Royal magical library", and only other option is opponents monster) Then play this card.

Graceful charity:
Same with "Dark world dealings" Wait until you have spare cards to discard. Also works very well with "Broww, huntsman of darkworld". Use other cards in hand first, as to maximise chance of discaring useless cards.

One day of peace:
Use immediately. (Hopefully put down "Royal magical library" first)

Pot of duality:
Depending on cards currently in hand, get whatever works in conjunction with them. Most needed cards are "Pot of greed" and "Royal magical library" (if you don't have a royal magical library yet) Do not get a "Toon table of contents", "Pot of duality", Toon world, or any piece of exodia" (Preferably)

Pot of greed:
Use immediately. (Hopefully put down "Royal magical library" first)

Spell power grasp:
Only use on "Royal magical library" when it's current spell counters are in 0 or 1. Retrieve spare "Spell power grasp" from deck and use for discarding.

Toon table of contents:
To lower amount of cards in deck and for spell counters, retrieve toon table of contents, then a toon world for discarding. If unable to get toon world or toon table of contents due to them already being in hand. Then you still get a spare card or two. (Also a spell counter for royal magical library)

Toon world:
Spare card for discarding or a free spell counter. (Preferably first option) (Not a necessary card)

Upstart goblin:
Use immediately. (Hopefully put down "Royal magical library" first)

All 5 pieces of the forbidden one: (Exodia)
Keep in hand, never discard or summon. (Needed to win game)

Broww, huntsman of dark world:
Free discard to draw one extra. Use in conjunction with dark world dealings and graceful charity only.

Royal magical libary:
Summon as soon as possible. (The only card you should summon) use in conjunction with everything in deck apart from the monsters. Activate effect when 3 spell cards are used. (Excluding spell power grasp)