If both players are required to perform actions simultaneously, such as by the effect of "Dark World Dealings", the turn player physically performs the action first, followed by the opponent, though both actions are considered to have occurred at the same time. In this example, the turn player must discard 1 card first, then, the opponent will discard 1 card, and the game will treat these two actions as having occurred simultaneously. 
When multiple Trigger Effects want to activate simultaneously, first determine whether or not the effect can be legally activated at that time, then the players will form a chain with these effects in accordance with the rules for simultaneous effects. These rules are colloquially referred to as Simultaneous Effects Go On Chain (SEGOC).
- Turn player's mandatory effects.
- Non-turn player's mandatory effects.
- Turn player's optional effects.
- Non-turn player's optional effects.
Both players each control a "Sangan", and a "Peten the Dark Clown". The effect of "Dark Hole" resolves, destroying all monsters on the field. The last thing to happen is the resolution of "Dark Hole", and all monsters on the field being destroyed, so all effects can be legally activated. Following the order for simultaneous effects, assuming that both players want to activate all their optional effects, we end up with the following chain:
- Chain Link 1: Turn player's "Sangan".
- Chain Link 2: Opponent's "Sangan".
- Chain Link 3: Turn player's "Peten the Dark Clown".
- Chain Link 4: Opponent's "Peten the Dark Clown".
As the opponent was the last one to activate an effect, the turn player has the first opportunity to activate a fast effect as Chain Link 5.
Player A activates "Super Polymerization", using their "Elemental HERO Shadow Mist" and their opponent's "Vanguard of the Dragon" to Fusion Summon "Elemental HERO Gaia". In this case, the last thing to happen is the Fusion Summon of "Elemental HERO Gaia", so the optional "when" effect of "Vanguard of the Dragon" cannot be activated. The mandatory effect of "Elemental HERO Gaia" is activated as Chain Link 1, and the optional effect of "Elemental HERO Shadow Mist" is Chain Link 2.
Effects which would activate simultaneously form a chain in accordance with the following priority levels:
- Priority Level 1: The effects of cards that activate mandatorily in that timing.
- Priority Level 2: The effects of cards that are face-up on the field or GY or are otherwise public which can be optionally activated in that timing.
- Priority Level 3: The effects of cards that are in the hand or Set or are otherwise private which can be optionally activated in that timing.
If multiple cards of the same player in the same priority level would be activated, they form a chain in the order prefered by the player.
If a card in the hand becomes public by some card effect, that card can be activated in the priority level 2 timing.
- You take battle damage whilst you have both "Gorz the Emissary of Darkness" and "Tragoedia" in your hand. Even though the Trigger Effect of both monsters are triggered, it is only possible to activate the effect of one of them, as both effects Special Summon themselves from the hand. 
- A face-up Beast monster you control is destroyed by your opponent's card effect and sent to the GY whilst you have one copy of "Green Baboon, Defender of the Forest" in your GY, and another copy in your hand. In this scenario, you can only activate the effect of one copy of "Green Baboon, Defender of the Forest". Even though one copy is being activated, and Summoning itself, from the GY, the effect is capable of activating in the hand, and thus the restriction applies.
- If you have both "Gorz the Emissary of Darkness" and "Ghostrick Mary" in your hand when you take battle damage, you can activate the effect of both monsters in chain. Even though the effect of "Ghostrick Mary" activates in the hand, it will never Special Summon itself from the hand.
- If you have multiple copies of "Trifortressops" in your hand, you can activate the effect of each copy in the same chain. The effect of "Trifortressops" is a Quick Effect, not a Trigger Effect.
- Yugioh TCG Rulebook v10 Page 50
- Problem-Solving Card Text, Part 7: 2012 Update – Conjunction Functions
- Fast Effect Timing
- OCG Perfect Rulebook 2017
- Card Rulings: Gorz the Emissary of Darkness
- Card Rulings: Tragoedia
- Card Rulings: Green Baboon, Defender of the Forest
- Ghostrick Mary jwiki
- Card Rulings: Trifortressops