The second era of Magic rules started in 1999 with Sixth Edition. Big changes included replacing the byzantine batch system of resolving spells and ailities with the stack, players losing the game immediately after their life total dropped to zero instead of waiting until the current phase ended and certain card types like Mana Source and Interrupt being removed from the game.
While the first era is primarily associated with the batch, the second one is mostly known as the "damage goes on the stack" era. Mercadian Masques was the first block designed in this era and Shadowmoor - the last. It ended after Magic 2010 introduced another set of major changes to how the game worked and got us into the modern rules era.
There are three aspects of the game that work differently in this era compared to modern Magic that I think are quite relevant for limited play. In decreasing importance, these are: combat changes, mana pool changes and finally changes to do with Lifelink and Deathtouch. While there are other rules that differ between this era and the modern one, these are less important so for the time being I won't mention them.
To write this I'll be using this guide and the 2009-02-01 Comprehensive Rules as these are the most recent official rules I found before the updates introduced in Magic 2010.
You can hover over any card in the examples below to see an enlarged version.
This is mostly relevant for when multiple creatures block a single attacker, in such a case the attacking player doesn't declare in which order their creature will deal damage.
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During the Declare Blockers Step, after blockers have been declared the attacking player declares which order their creature will deal damage to the creatures blocking it.
If an attacking creature is blocked by multiple creatures, the attacking player assigns damage however they wish among the creatures blocking it. This happens at the start of the Combat Damage Step.
The attacking player assigns damage their creature deals among defenders however they wish.
If the attacking player wants to assign damage to a creature blocking one of their creatures, they need to have assigned lethal damage to every blocking creature that precede it in the order announced during the Declare Blockers Step.
The damage goes on the stack as originally assigned. Afterwards players can play spells and activate abilities before damage resolves.
Players get to play spells and abilities after damage is assigned, but before it's dealt.
Once damage is assigned, it's dealt immediately, only then do players get priority.
When a phase ends any unspent mana left in a player's mana pool is lost, mana is not lost this way when steps end.
Mana can be used throughout a phase and is only lost at the end of that phase.
Mana pools empty at the end of steps and phases.
When unused mana is lost from a player's mana pool, that player loses life equal to the amount of mana lost this way.
Loss of mana causes loss of life.
Loss of mana doesn't cause loss of life.
When a creature with lifelink deals damage, the triggered ability goes on the stack and the player gains life only when it resolves.
The lifelink trigger needs to resolve before gaining its controller life.
When a creature deals damage, its controller gains life immediately.
When a creature with deathtouch deals damage, the triggered ability goes on the stack, any creatures it dealt damage to will be destroyed only when this ability resolves.
A creature dealt damage by a creature with deathtouch will die once the deathtouch trigger resolves.
A creature dealt damage by a creature with deathtouch will die the next time state-based actions are checked.