There are many types of effects in this game: Ignition, Trigger, Quick, Continuous, Lingering, and Unclassified.
This article covers what each type means, as well as how to identify them.
Ignition (Activated - Spell Speed 1) (negatable)
About: Ignition Effects can only be activated during your Main Phase. They are Spell Speed 1, meaning that you can't chain them to anything. Because of this, you can only ever have 1 Ignition Effect in a Chain.
Identifying them: These are Activated Effects, so their PSCT features a colon ( : ) and/or Semi-colon ( ; ). Furthermore, they will (usually) start with "You can", "Once per turn:", or "During your Main Phase".
Breaker the Magical Warrior's effect to destroy a Spell/Trap.
Machina Gearframe's effect to Special Summon itself or Equip itself.
Dark Grepher's effect to send a card from your deck to the GY.
Trigger (Activated - Spell Speed 1) (negatable)
About: Trigger Effects can only be activated when their Trigger Condition is met.
They are Spell Speed 1; they cannot be chained to other effects.
If their Trigger Condition is met, they will activate on a new chain. When multiple Trigger Effects happen at the same time, use SEGOC to order them.
Phase-Based Trigger Effects
Trigger Effects which happen at a specific phase (such as Lightsworn's End Phase Mill, Spirits returning to hand, Bujin Yamato's search, or Gladiator Beast's 'tag-out'), do not chain to each other. These effects happen one after the other, each on their own chain.
🔗 Early Trigger
In older formats, trigger effect ordering is more complicated. You can read about that here.
Identifying them: These are Activated Effects, so their PSCT features a colon ( : ) and/or Semi-colon ( ; ). They always start with their Trigger Condition - usually a "when ..." or "if...".
These can sometimes be confused with Quick Effects, especially for cards without PSCT.
Gladiator Beast Laquari's effect to Special Summon.
Sangan's effect to search a card.
Both of Elemental HERO Stratos' effects.
Quick (Activated - Spell Speed 2) (negatable)
About: Quick Effects can be activated at any time that a player has priority to activate an effect. As they are Spell Speed 2, they are fast effects, and can chain to other effects.
Identifying them: These are Activated Effects, so their PSCT features a colon ( : ) and/or Semi-colon ( ; ). Modern PSCT for these cards features the phrase "(Quick Effect)". Some older PSCT for them features the phrase "(This is a Quick Effect.)".
Before that, it was written as "During either player's turn, ...". In very old text, there is no indicator for Quick Effects (called "Multi-Trigger" at the time).
Light and Darkness Dragon's effect to negate a card activation.
Zoodiac Drident's effect to destroy a card on the field.
Honest's effect to make a monster gain ATK.
Continuous (Not Activated) (negatable)
About: Continuous Effects constantly apply, as long as the card is on the field. (It must be in its correct Zone - EG, Jinzo's effect doesn't apply while equipped to "Relinquished". But also Machina Gearframe's effect to protect a monster from being destroyed (S/T is the "correct Zone" for it when it equips itself).
Identifying them: These effects Do not Activate, so they can be identified via their lack of colon/semi-colon. However, Lingering and Unclassified effects are identified in the same way, so it can sometimes be hard to tell which is which. If it's an effect which only applies on the field - like Jinzo - there's a good chance that it's continuous.
Spirit Reaper's effect to prevent itself from being destroyed by battle.
Banisher of the Light's effect to banish monsters sent to the GY.
Ancient Gear Golem's effects to pierce and to prevent the use of Spell/Trap cards.
About: "Lingering" is not an official game term. However, it's useful, so I have included it here.
Lingering effects are effects which have already applied, but are still doing something. If the effect is applied to the card which caused the effect, it can be negated. Otherwise, it can't be negated, once it has applied. You can read more about that here. (EG - If a monster changes control via "Mind Control", and is then affected by "Forbidden Lance", it still returns in the End Phase).
Identifying them: These effects Do not Activate, so they can be identified via their lack of colon/semi-colon.
Oftentimes, lingering effects are things which happen when the physical card is already gone - for example, once Brain Control has already finished resolving, or Examples:
"Until the End Phase" as seen on "Brain Control" and "Rush Recklessly".
Effects given to Tokens, EG"Deus Token"'s "cannot destroyed by battle".
"Destroy it during the End Phase"as seen on "Limiter Removal".
Unclassified (Not Activated) (negatable)
About: Unclassified effects are officially "Effects which are none of the above". These effects are similar to Continuous Effects, but can apply anywhere - not just on the field.
Identifying them: These effects Do not Activate, so they can be identified via their lack of colon/semi-colon. However, they are notoriously hard to identify past that. Oftentimes you will just have to search using RoboMika or Yugipedia to see if it's unclassified.
Grapha's effect to Special Summon itself from the GY.
Machina Fortress' effect to Special Summon itself from the hand/GY.
Grandsoil's effect to make you skip your Battle Phase.
Conditions (Not Activated) (not negatable)
About: Conditions aren't really effects. In the OCG, they're often called "Rule Effects". Conditions can't be negated and do not activate. They always apply, theoretically in every zone of the game.
Identifying them: These effects Do not Activate, so they can be identified via their lack of colon/semi-colon. However, they are notoriously hard to identify past that. Oftentimes you will just have to search using RoboMika or Yugipedia to see if it's a condition.
Quickdraw Synchron's condition, preventing it from being used as Synchro Material.
"Cannot be Normal Summoned/Set Must first be...", as seen on Gigantes.
"You can only activate this card/effect once per turn", as seen on many new cards.
A note on Spell/Trap effects
Sometimes, you will see words like "Trigger-like" and "Continous-like" be used to describe the effects of Spell/Trap cards. These terms are unofficial and, in my opinion, useless.
"Trigger-Like" just means that the effect functions in the exact same way as a Trigger Effect, but is on a Spell/Trap card, not a monster card.
There is absolutely no difference between Trigger Effects and "Trigger-Like" effects - just that one is on a monster, and the other on a Spell/Trap.