Fusion Summoning is the act of Special Summoning a Fusion Monster from your Extra Deck using "Polymerization" or any other card effects which explicitly state the Summon is a Fusion Summon.

How to Fusion Summon

To Fusion Summon using "Polymerization" you must have the Fusion Material listed on the Fusion Monster in your hand or on your side of the field or a combination of both. You then activate "Polymerization", next select the Fusion Monster from your Extra Deck, next send the Fusion Material to the Graveyard, then you Special Summon the monster to your side of the field.
For example, to Fusion Summon "Flame Swordsman" using "Polymerization" you must have "Flame Manipulator" and "Masaki the Legendary Swordsman" (the Fusion Material) either on your side of the field and/or in your hand. You then activate "Polymerization", select "Flame Swordsman" from your Extra Deck, send the Fusion Material to the Graveyard and Special Summon "Flame Swordsman".

Advanced Rulings

If a monster is Special Summoned from your Extra Deck by a card effect, it is not treated as a Fusion Summon, unless stated on the card. For example, Special Summoning a monster from your Fusion Deck using "Cyber-Stein" is not considered a Fusion Summon.

Normally Fusion Monsters cannot be Special Summoned from the Graveyard or Removed from Play Zone unless they were properly Fusion Summoned before being sent. You cannot use "Re-Fusion" to revive a Fusion Monster that has been Special Summoned using "Cyber-Stein" or sent to the Graveyard by "Fusion Guard". Monsters Fusion Summoned can be revived using cards like "Re-Fusion" unless stated otherwise.

Alternate Methods

Other than using "Polymerization" cards can be Fusion Summoned using any of the following cards. Be sure to follow the instructions on the card to Fusion Summon the monster correctly.