To kick things off, we're going to talk a little bit about The Stack. Most players have probably heard about the Stack, and even those who've not heard the term will still probably recognize it as a core mechanic of Magic gameplay. Section 405 of the Comprehensive Rules tells us just what the Stack does and how. In short, all Spells cast and Abilities that are Triggered or Activated (except Mana Abilities, Rule 605) go onto the Stack. The Stack keeps things ordered for you during the game, operating in Last-in-First-Out order. New objects being placed on the Stack go on top of any objects already on the Stack. When there are spells and/or abilities on the Stack and both players pass Priority, the top-most object on the stack resolves.
How about a quick example of the Stack in operation? You control a Grizzly Bears. Your opponent casts a Lightning Bolt, targeting your Grizzly Bears. The Lightning Bolt is put on top of the Stack and waits to resolve. You then receive Priority to act and decide that you'd like to save your Grizzly Bears so you cast Giant Growth, targeting the bear. Your opponent has nothing else to do, so you both pass Priority. With Giant Growth on top of the Stack, it resolves, making your bear 5/5. Next Lightning Bolt resolves, dealing 3 damage to your now-giant bear. 3 damage is marked on the bear, but it survives the bolt and the game goes on!
Much like targeting the bear with a well-timed Giant Growth to save it from the Lightning Bolt, you can target spells and abilities which still reside on the Stack with certain spells. Voidslime, for example, targets an object on the stack, countering it and removing it from the stack so it does not resolve. Likewise, spells such as Reverberate make copies of spells on the Stack, which can be a bit more difficult to understand. Let's look at a simple example of that.
It's your turn, the Stack is empty and you cast a Lightning Bolt, targeting your opponent's Grizzly Bears so Lightning Bolt goes on the stack. The opponent responds by casting Giant Growth on the bears, which goes onto the Stack above the Bolt. You respond by casting Reverberate, targeting the Lightning Bolt and Reverberate goes on the stack. Now both players pass priority and Reverberate resolves. When it resolves it puts a copy of Lightning Bolt onto the Stack, allowing you to choose new targets if desired. You decide not to change the target, so it's targeting the Grizzly Bears. Both players pass priority again and your Copy of Lightning Bolt resolves dealing 3 points of damage to the Grizzly Bears. Before either player receives priority, State-Based Actions are checked and Grizzly Bears is destroyed because its toughness is 2 and it has 3 damage marked on it from the copy of Lightning Bolt. Both players pass priority again and Giant Growth tries to resolve. Since the only target for the spell no longer exists, it is countered on Resolution. Finally, when both players pass priority again, Lightning Bolt is handled with the same effect.
I've used the word Priority a lot in this article, but we haven't actually said what it means. You can read up on Priority in the Comprehensive Rules section 116, but I'll summarize here for you now. In short, only the player with Priority can cast spells and activate abilities. Who has Priority? Well there are guidelines for determining who should receive priority at any given time. At the beginning of each Step and Phase, the Active Player, or whoever's turn it currently is, will receive priority first. After casting a spell, whoever had priority when the spell was cast will receive priority again after it is cast. i.e. you get a chance to respond to your own spells before your opponents get a chance to. Also, after a spell or ability resolves, the Active Player receives priority.
One frequent Priority confusion that I see a lot of from even experienced Magic players is the notion that an Instant can be cast at any time. To be sure, an Instant spell can be cast only any time that you have priority. While it may seem nitpicky, here is an example where it is crucially important.
A player casts Venser, the Sojourner. The spell resolves and the Planeswalker is put onto the battlefield with 3 Loyalty counters. The non-active player then decides to Boomerang the Planeswalker to prevent him from using his ability. This can not happen! After the Planeswalker resolves, the Active Player receives priority. That player must either cast a spell, activate an ability, or pass priority before there is ever an opportunity to cast Boomerang on Venser. The best you could do is wait until his ability is activated, then Boomerang him, though as per 112.7a, "Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won't affect the ability." As such Venser's ability would still resolve, even after being returned to the hand.
Have you ever run into difficult situations with the Stack that seemed like an endlessly complicated mess? Tell me about it in the comments. I do love a challenge!