Wizards did a major revamp of the MtG rules with the release of 6th Edition. (Since then there have been very few changes, mainly minor.) The major changed areas are:
The Stack. This is where all spells, activated abilities and triggered abilities go. It's a Last In, First Out stack. So "in response, I do X" just means "with that on the stack, I put X on top of it". Before the top thing resolves, all players get priority in turn, and may put instants or activated abilities on the top of the stack. If nobody does, the top thing resolves. It still mostly works the way it used to, but differences include:
All interrupts and fast effects are now errata'ed to be instants, and there's no concept of "interrupt" now. Everyone can always respond to anything you put on the stack.
Tapping lands/creatures for mana doesn't use the stack and can't be responded to. Nor can playing a land.
You can let something resolve from the stack without letting everything resolve. Eg: you play a Fireball at me for lethal damage. I respond by adding MTG: Impulse to the stack; let that resolve; and then add the MTG: Counterspell to the stack which I just drew from the Impulse.
You don't have to worry about a separate interrupt stack resolving before the instants stack can continue. There's no concept of "series" or "batches".
Upkeep abilities are almost all worded as abilities which trigger "At the beginning of your upkeep" now. They all go on the stack (you choose the order), then you may respond to some or all of them; then when they're all done resolving, both players get priority, and if nobody does anything you move on to the draw step.
Damage-prevention abilities can be played at any time. The text on MTG: Samite Healer and similar reads "Prevent the next 1 damage that would be dealt to target creature or player this turn." There's no "damage prevention" or "damage redirection" step any more. Prevention abilities set up a "shield" which sits there until end of turn, or until it gets used up.
Regeneration also can be played at any time, and sets up a shield which modifies "the next time this creature would be destroyed this turn" into "instead tap it, remove all damage, and (it it's in combat) remove it from combat". In particular, you can pay to set up a regen shield at any point, not just when the creature's about to be destroyed. Note that the creature won't tap or actually regenerate until it would die, though.
Tapping creatures once they're in combat has no effect (well, doesn't stop them attacking or dealing damage). Instead, you have to tap someone's creature before the "declare attackers" step of the combat phase. The combat phase has 5 steps: "beginning of combat", "declare attackers", "declare blockers", "combat damage", and "end of combat". Instants and activated abilities can be played during each step. To stop a creature attacking, you have to tap it before attackers are declared. To stop a creature blocking, you have to tap it before blockers are declared.
Combat damage also uses the stack: so it gets assigned, then either player can also play instants or activated abilities before it resolves (eg variants on MTG: Unsummon or MTG: Terror). When damage resolves from a creature that's no longer in play, it's still dealt as far as is possible.
So, in usual use, you can declare an attack or block - then use abilities that cause you to tap. To prevent attack or block, do it in reply to declaring an attack - before they say what with. And to stop a critter dealing damage - kill it ASAP. --Vitenka
End Of Turn effects: there is a subtle and usually-irrelevant distinction now between "Until end of turn" (eg MTG: Giant Growth) and "At end of turn" (eg MTG: Sneak Attack)...
"Until end of turn" effects will always end on the same turn that they started.
"At end of turn" effects can actually trigger at the end of the next turn after the turn they were played. This is because "At" indicates a triggered ability, which triggers in this case at the beginning of the "end of turn" phase.
For example, a combination which was used quite frequently in tournaments when it was legal which exploits this trick: MTG: Astral Slide can "remove target creature from the game. Return that creature to play at end of turn". If you use this ability during the "end of turn" phase, then the next time the "at end of turn" words would apply is at the end of the next turn.
Legend and Wall Rules
With CHK (so during the lifetime of 8th Edition) Wizards eliminated the Legend creature type in favour of a Legendary supertype for creatures, and changed the Legend rule. It now reads:
420.5e If two or more permanents with the same name have the supertype legendary, all are put into their owners' graveyards. This is called the "legend rule." If only one of those permanents is legendary, this rule doesn't apply.
They also eliminated the Wall rule, instead giving most existing walls a new ability: Defender (This creature can't attack).
As has been alluded to above, large amounts of older cards have been given errata now. Mostly the errata doesn't affect functionality, but in some cases it does. You can get hold of the updated wording ("Oracle" wording) at any of these places:
CrystalKeep?'s [rulings search] lets you see Oracle wordings for cards searched by all sorts of criteria including RegExps. It is now (Sep '06) being kept up to date again.
The official [Oracle page] is the ultimate authority, except when it makes mistakes.
Protection from all sorts of things exists now - protection from red, protection from creatures, protection from artifacts, etc. Protection from [quality] means four things, abbreviated DEBT:
Damage from sources with that quality to the permanent with protection is prevented.
Enchantments with that quality can't enchant the permanent with protection, and Equipment (a new artifact version of creature enchantments - see [here]) with that quality can't equip the permanent with protection.
It can't be Blocked by creatures with that quality.
It can't be Targeted by sources with that quality while it's in play.
Trample: you now have to assign damage to all blockers before you can trample any over to the defending player. You have to assign at least as much as would be necessary to kill it, even if the damage will be prevented or the creature is going to regenerate. Eg a 5/5 black trampler gets blocked by a 2/2 protection-from-black MTG: White Knight and another 2/2 creature. At most 1 damage may be trampled over to defending player, if the attacker assigns 2 damage to each blocker; if the player expects a MTG: Giant Growth or whatever, he can assign more than that to one or other creature, even all 5 to one of them. Any damage assigned to the White Knight will be prevented when combat damage resolves.
Madness now requires you to play the card as part of its resolution, rather than until you pass priority. (In other words, it now works as non-experts have probably always played it). The explanation in the [Time Spiral rules changes] page is very readable.
From Time Spiral, +1/+1 and -1/-1 counters eliminate each other as a state-based effect. Other counters are unaffected.
We can provide more details on any specific abilities on request. Note in particular that there are now abilities for several common concepts that previously took lots of words to spell out on each card, such as "haste" (unaffected by summoning sickness), "reach" (can block flyers), and so on. There's a handy 1-page cheat sheet of these keyword abilities [available here] (PDF).
In recent years there have been two new card types (like "Instant" and "Creature") and two important new subtypes. These are:
Tribal: Irritatingly, although the word is an adjective, the fact it's a type means it's a noun. As in "This card is a Tribal". Ignore that. It's simply a means to get creature types onto non-creature spells. For instance MTG: Tarfire is a "Tribal Instant - Goblin". As such, it costs 1 less to play if MTG: Goblin Warchief is in play, and can't target MTG: Warren-Scourge Elf. This type was properly introduced with Lorwyn (autumn 2007), and it is not clear whether it will exist in as much strength in the future.
Planeswalker: Also introduced with Lorwyn was a cycle of five Planeswalkers. We know more will be printed, although not especially often. See MTG: Garruk Wildspeaker for an example. The rules are not short, but fairly easy to understand. See [here] for Wizards' own explanation.
Equipment: This is really new. Mirrodin block (2003-04) introduced this new subtype of artifacts. See MTG: Bonesplitter for the canonical example. In effect, it works similarly to Auras except that:
Equipment does not come into play attached to any creature.
You may pay the Equip cost any time you could play a sorcery to attach the equipment to a creature you control. This includes being able to move it from one creature to another, but not being able to completely remove it from all creatures.
If the equipped creature leaves play, the equipment stays in play, attached to nothing.
All I can give here is subjective comments from people...
Can you tell me how tight tourneys are on the 'do you respond' rule? Because I just know I'll forget at least once. And how considerate are players of slower players? Because I'll want to read every card... Obviously asking generalisations - but how 'nice' is the magic tourney community in general. --Vitenka (We need to know!)
Magic tourney community in general? Hard to say. But prerelease and sneak preview tournaments are pretty much the most relaxed tournaments there are, with regards to rules issues. I've often been allowed to take moves back by my opponent (although you shouldn't expect to be able to). There are occasional gits who're pedantic to the point of frustration, but mostly people at prereleases and sneak previews are very friendly and informal about precise timing rules. --AlexChurchill, who was slightly surprised himself when he first found this out
And for similar reasons, prereleases/sneak-previews are pretty tolerant of people having to read each card. The whole point of P/SP tournaments is that they're a chance to play with cards which nobody has ever played with before. Thankfully, they don't expect everyone to have read the spoilers which get leaked about 3 days beforehand on sites like mtgnews.com .
Oh - tourney play probably involves being very very anal about [the stack and responses], and giving a chance for the opponent to respond at each step (which is only courteous) and making damn sure that you do respond when you need to. --Vitenka (just guessing, and hoping that's changed)
The major change that affects my playstyle has been the continual shortening of matches - you have to have an early game strategy, you can't just weather it and then hit them. Combined with that, the massive number of combos and people setting up vital combos to win really frustrates me. Used to be there were very very few instant win combos conceivable - and all but one were impractical. (And the one used two limited cards and was banned quicksharp. So you had to use a second mana store artifact...) --Vitenka
In Limited play (i.e. prerelease) this won't be a problem - I believe it is not really a feature of T2 at the moment - but it certainly is in T1 and Extended. There's a distinction to be made between cards with great synergy (MTG: Astral Slide, MTG: Lightning Rift) and 'instant win' combos (MTG: Pandemonium, MTG: Saproling Burst) - mostly in that the former is interesting to play against, and the latter is not. IMO, anyway. -- TheInquisitor
Yes, much less of a problem in sealed. I was thinking of combos of the "This card plus this card causes infinite recursion" type. Infinite turns being best, followed by infinite draw then infinite mana - but all being basically 'and I win'. --Vitenka
Those do look fairly sick. Shouldn't things as big as that have disadvantages? Anyway, message got - play creature removal. Especially since sealed is liable to take longer to finish, and so that much mana is more likely to come up. Mmm.. corollary - play mid-sized creatures because the opponent won't want to waste removal on them, just in case I have a truly big one in hand. --Vitenka
Belated report from a tourney... Most magic players are tolerable. Some are intolerable enough to make me discard the game again. --Vitenka