Monster effects generally activate during your turn, either during your Main Phase or during the Battle Phase.
Exceptions:
* Some monster effects activate during your opponent's turn. These effects will usually have a specific trigger, such as your opponent summoning a monster or activating a spell/trap card.
* Some monsters have effects that activate during either player's turn. These effects will usually have a condition that must be met, such as having a specific card in your hand or controlling a specific type of monster.
Here are some examples:
* "The Winged Dragon of Ra" has an effect that allows you to add cards from your Deck to your hand during your opponent's turn.
* "Cyber Dragon" has an effect that allows you to Special Summon a Cyber Dragon from your hand during either player's turn.
* "D.D. Crow" has an effect that activates when a monster is Special Summoned and allows you to send it to the Graveyard.
In general, if a monster effect does not specifically state that it can be activated during your opponent's turn, you cannot activate it.