Welcome back, I guess? Let's continue with the previous priority article. What, you forgot already? Something about tennis balls? Yeah, probably...
Now that you (hopefully) understand more about what priority really is, let's go into a more practical point of view. It sure is nice to know about it, but there's no point if one can't use priority for something, right?
Like the definition said, priority allows you to perform certain actions before the opponent does. Most of these actions are performed automatically using priority, such as a Normal Summon, and it's confusing to even think of it. So let's go into something that heavily uses priority: Activating an effect. As mentioned, priority only allows you to perform this action before the opponent does, but it does NOT allow you to resolve your effects before either player can respond. For example, if I wish to activate the effect of Chaos Sorcerer targetting Sangan, and my opponent wishes to activate Torrential Tribute to get Sangan's effect as well as getting rid of my monster, priority will only allow me to activate Sorcerer's effect as link 1, but it will not Remove Sangan from Play before the tidal wave can be invoked. In other words, priority allows your effects to appear on an earlier chain link, but due to the rules of chaining, an earlier link resolves later. In most cases, this is the main use you'll give to priority: Activating Ignition Effects before the opponent destros your monster.
So, exactly, for how long does the player have priority? The turn player retains it until he or she activates an effect with Spell Speed, or wishes to pass priority. The first case is simple: Any effect that uses the chain has Spell Speed, such as activating a Trigger Effect, a Continuous Spell Card, or a Continuous Trap Card. Activating any of these will pass priority to the opponent. The other situation is when the player simply passes priority to the opponent, allowing him or her to respond first to a given event. Remember the stubborn tennis player who refused to serve? Now that player asks his opponent if he would like to serve instead this time.
Passing priority is also very common, but rarely noticed by the players. For example, in order to move through your turn, from Phase to Phase, both players have to agree that no one is going to perform any actions, by passing priority. When both players pass priority, they choose not to respond, and so, the game progresses: If you were building a chain, you resolve it (as mentioned above). If you are within a Phase, that Phase is over. If an attack was declared, the attack goes through. Some times, it's even strange to consider that you had priority, such as when you have priority to negate your own Normal Summon. Not too tempting, is it?
There's also the pestering case of Trigger Effects. Trigger Effects have some really notable rulings, but I'll leave those for an article about them. What should be noted now is that if the turn player activates a Trigger Effect (being the last thing to happen), then priority is passed immediatly to the opponent, regardless of how anxious the turn player was to respond. This tends to be quite common: One doesn't need to go any further than Caius the Shadow Monarch, or the infamous Breaker the Magical Warrior. When they are Normal Summoned, their Trigger Effect activates, and priority is immediatly passed to the opponent to respond. Also, note that Trigger Effects always activate earlier than Ignition Effects, and these, in turn, can't be activated as they can't be chained to Trigger Effects (or anything). In other words, Trigger Effects really mess up priority, but they never erase it. They may change who has priority, or what kind of actions you can perform. Of course, if your opponent's Trigger Effect is the last thing to happen, then priority will be retained by you.
I believe that's pretty much all that there is on priority. It's much easier to understand when you think of it as a right of the player to perform actions, than as a magical effect attached to a bunch of monsters that disrupts the order of a chain by yelling "PRIORITY" as loud as possible. One final note would be reminding that, since priority is a right, you don't need to announce it, or be concerned that it may be "stolen", or even "negated" like some people say. When you wish to use it, simply announce it as the means to your end: "I activate Rescue Cat's effect by using priority". It's as simple as that. It's not a race on who sends the Cat or Book of Moon to the Graveyard faster.
If you have any questions, feel free to drop me an e-mail at ness00[at]gmail[dot]com.