Priority

Interpreting Priority is what can turn a Good Player into a Great Player.

Take the following Scenario:

Player A has a face-up D.D. Warrior Lady. He sets a face-down Spell/Trap Card, and ends his turn. Player B Normal Summons Exiled Force. Player A activates Trap Hole.

Here, Priority falls to Player B, seeing as he is the Turn Player. Summoning a Monster does not have a Spell Speed, and thus Player A cannot chain Trap Hole in response to it. Player B chooses to activate Exiled Force's Ignition Effect. Player A has effectively chained Trap Hole to Exiled Force's effect, which is Spell Speed 1.

Player B successfully Tribute's Exiled Force to Destroy Player A's D.D. Warrior Lady. Player A's Trap Hole no longer has a Target, and thus cannot Resolve

As a general rule of thumb, Ignition effects can be activated as soon as the monster hits the field, via a Successful Summon. The opposing player may chain a Spell or Trap Card to destroy the monster, but since a Summon cannot be chained to, he/she must chain to the effect, if the turn player chooses to activate it. Since an activated Spell or Trap Card resolves first, the monster with the effect would be destroyed, but unless the Spell/Trap Card negates the effect of the monster, the Effect would still Resolve, even if the monster wasn't on the field.

The most important thing to understand, is that, unless a monster card has a Multi-Trigger effect, a monster card cannot have priority, since their effects are all Spell Speed 1, and thus cannot be used against anything. The Turn Player, however, always has priority with an Ignition Effect.