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How to Fusion Summon
A player can Fusion Summon a Fusion Monster from the Extra Deck by activating a card or effect that performs a Fusion Summon. When that effect resolves, the player uses appropriate Fusion Materials listed on a Fusion Monster by moving them from some location(s) to another location, as specified by the effect performing the Fusion Summon (usually sending them to the Graveyard or banishing them). After that, the player Summons the Fusion Monster from the Extra Deck to an unoccupied Main Monster Zone that a Link Monster points to or an Extra Monster Zone in face-up Attack or Defense Position.
Even if all appropriate Monster Zones are occupied, a Fusion Monster can still be Fusion Summoned as long as at least one of the Fusion Materials used is in one of these Zones, so that there is an available Zone when the Fusion Monster is Summoned.
List of cards that Fusion Summon
Example A: Normal method
Example B: Using Fusion Substitute Monsters
+ a correct Fusion Material
("Elemental HERO Sparkman")
Example C: Using a monster as both a Fusion Material and to conduct a Fusion Summon
A Fusion Material with an effect that Fusion Summons
("D/D Swirl Slime")
+ A Fusion Material
Like other Extra Deck monsters, if a Fusion Monster is not Fusion Summoned first, it cannot be Special Summoned from the Graveyard or while banished (unless it specifies another way to properly Special Summon it, in which case it must first be Summoned that way).
For example, if a Fusion Monster is Special Summoned from the Extra Deck by the effect of "Cyber-Stein" and sent to the Graveyard, or was sent to the Graveyard by "Fusion Guard", it cannot be Special Summoned from the Graveyard by "Re-Fusion"; however, if it was originally Fusion Summoned by "Polymerization", it can be Special Summoned from the Graveyard by "Re-Fusion".
In the anime
While visual depictions of Fusion Summons have varied significantly among the different anime series, most generally show the Fusion Materials, or their cards, being warped into particles or forms of energy in a spiral direction, which then merge with each other within a spiraling portal, from which the Fusion Monster emerges. It is not until Yu-Gi-Oh! ARC-V where a standardized version of this method is adopted for all Fusion Summons, with the portal consisting of blue and orange swirls of energy, referencing the artwork of "Polymerization", and the Fusion Material Monsters transforming into differently colored forms of energy (usually the colors being contrasting ones like blue/red, yellow/violet, etc.), which then swirl together into a spiral before entering the portal. Fusion Summon practitioners usually clasp their hands together at the moment the monsters combine, seemingly mirroring that the materials become one.
Prior to ARC-V, another depiction of Fusion Summon, notably used for "Dark Paladin" and "Dragon Knight Draco-Equiste", shows the Fusion Materials being engulfed in a sphere of energy, which then disperses to reveal the Fusion Monster. Other times, the Fusion Monster emerges from a fierce whirlwind.
In Yu-Gi-Oh! VRAINS, Fusion Summoning is more visually elaborate. The Fusion Materials transform into streams of colored particles similar in shape to the energy forms seen in ARC-V, swirling together and then bursting into multiple vortexes of the same color as the Fusion Materials, which twist around one another and combine into one, from which the Fusion Monster appears.
In the Yu-Gi-Oh! anime, under Battle City Rules, which applied during the Battle City tournament, Fusion Monsters cannot attack the same turn they are Summoned. This is exemplified in episode 65, when Strings uses "Quick Attack" on "Humanoid Worm Drake" to bypass that rule in his Duel against Yami Yugi. This rule does not exist in the OCG/TCG and was removed for all subsequent series.
In Yu-Gi-Oh! ARC-V, a Fusion Summon performed using Fusion Materials that have been previously Pendulum Summoned is referred to as a "Pendulum-Fusion".