THE STACK

Whenever you play a spell, it goes onto the STACK until it resolves. If your opponant decides that they want to respond to your spell, thier spell goes on the stack on top of your spell, and thier spell resolves first.
Unless, of course, you decide to respond to thier spell, in which case your response would go ontop of thier response and resolve first.
Unless, of couse, they decide to respond. . . See, it can be very confusing. Let's have a demonstration.

Ex.1
Player one plays a creature.
The spell goes on the stack, and waits for a response.
player two decides not to respond.
The spell resolves, and becomes a creature.

Ex.2
Player one plays a creature.
The spell goes on the stack, and waits for a response.
Player two responds, and attempts to counter the spell.
Player two's counterspell goes on the stack, and waits for a response.
Player one decides not to respond.
The counterspell resolves, sending player one's creature spell to the graveyard.

Ex.3
Player one plays a creature.
The spell goes on the stack, and waits for a response.
Player two responds, and attempts to counter the spell.
Player two's counterspell goes on the stack, and waits for a response.
Player one responds, and attempts to counter player two's counterspell.
Player one's counterspell goes on the stack, and waits for a response.
Player two decides not to respond.
Player one's counterspell resolves, sending player two's counterspell to the graveyeard.
Player one's spell resolves, and becomes a creature.

This is how "instant" spells work, they are normally played in response to other player's spells or abilities. The best players know exactly when to play thier spells, and they have no trouble saving them if it isn't exactly the right time to play them.

TIPS
If you have an Instant spell in your hand that affects you only, save it until end of turn. You might need that mana for something else.
If you have an Instant spell in your hand that deals damage or kills things, the best time to play it is when your opponant taps his attackers. That way, he won't be able to say "oops, I'm not attacking with that" or weasel his way out of losing a creature.
If you have a counterspell in your hand, save it for a spell that you really don't like. Don't waste it on something petty.

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