A Special Summon is any Summon other than Normal Summon or Flip Summon. They only occur due to game mechanics, Card Effects, or Summoning conditions.
Unlimited Number of Summons
There is no restriction on the number of times you can Special Summon in a turn;
Special Summons do not take up your Normal Summon/Set. Also, unless otherwise specified, Special Summoning high-Level Monsters does not require Tributes.
Ritual Summons, Fusion Summons, Synchro Summons, XYZ Summons, Pendulum Summons, and Link Summons are all considered Special Summons.
Special Summon types:
Built-in Special Summon
By an Effect that does not activate
Special Summon with a Card Effect
Special Summon types
There are two different types of Special Summons. The type indicates which Cards and Effects can respond to or negate the Special Summon. Cards printed with Problem-Solving Card Text can easily have their method of Special Summon determined: Effects that contain a colon or semicolon are Special Summons due to a Card Effect (and thus start a Chain), and Cards that don't have a colon or semicolon are built-in Special Summons.
Built-in Special Summon Built-in Special Summons (unofficially known as inherent Special Summons) are Special Summons that are done by game mechanics or the Monsters' own Summoning condition (e.g. Contact Fusion) or Summon Effect. These Special Summons do not start a chain.
Normally, you can only perform such a Summon during an open game state in your Main Phase. They are never performed as part of an Effect resolution; Effects that cause you to perform one of these Summons instead have you perform the Summon immediately after they resolve ( "Formula Synchron" or "Advanced Heraldry Art"), and are actually Special Summons with a Card Effect that treat the Summon as a Built-in Special Summon.
There are two sub-types of Built-in Special Summon: Summon by Conditions and by Effect that does not activate.
These Special Summons are exclusive for Special Summon Monsters. Special Summon Monsters must be Summoned by following their condition(s) first in order to be considered properly Special Summoned.
An Example is “Photon Thrasher”.
These Special Summons are not Card's Effect, so Cards like "Vampire Grace" cannot be used in response.
Synchro Summons, XYZ Summons, Pendulum Summons, Link Summons, and Contact Fusions are all considered Special Summons By Condition.
By Effect that does not activate
Special Summon Monster Effects are Effects that allow that Monster to be Special Summoned. These Special Summons are optional.
These Effects are an Unclassified Effect, as they do not activate (like Ignition or Trigger), and they are not Continuous Effects.
An Example is “Cyber Dragon”.
By Card Effect
Special Summons by Card Effect are Special Summons that occur during the resolution of an activated Card Effect (for example "Monster Reborn"). Ritual Summons and Fusion Summons are both types of Special Summoning with a Card Effect.
These Special Summons cannot be negated. However, you can prevent them from occurring in the first place by negating the Effect or Card that would perform the Special Summon.
While they are rare, Special Summons as the result of an activated Card or Effect that do not occur during that Effect's resolution also fall into this category. Cards such as "Revival Jam" and "Memory of an Adversary" can perform this kind of Special Summon.
Some Effects that Special Summon can ignore the Summoning conditions of the Summoned Monster, allowing them to Special Summon Monsters regardless of their Summoning conditions.