Most of you should already know this but I have run into several people in the last few days who don't understand how Double Strike works. Some of the common misconceptions I have run into are...
1) double strike deals double the creatures power in damage during combat.
2) Being blocked and the blocker dying during first strike stops the regular strike from happening.
So here is a brief review of the reality of Double Strike.
At its most basic level Double Strike is First Strike and Regular Strike all on 1 creature.
So let's use Fencing Ace example.
Example A
You attack with Fencing Ace and your opponent does not block. Fencing Ace will deal 1 damage in the first strike combat damage step and then 1 more in the regular combat damage step.
Example B
You attack with Fencing Ace and you opponent blocks with a Llanowar Elves. Fencing Ace will deal 1 damage in the first strike combat damage step to the Elves killing it and the Elves will go to the graveyard. Then in the regular combat damage step Fencing Ace attempts to deal 1 damage but there is no longer a creature for it to do damage to but it has been blocked. This results in no damage being dealt (the Fencing Ace in essence swings and hit the air where the Elves had been standing. The exception to this is if Fencing Ace had been given Trample. Trample allows damage beyond the toughness of the blocker(s) to be assigned to the player. Thus, if our Ace had trample the regular combat damage would still happen even though the Elves was dead and this 1 point could be dealt directly to the player.
I hope this clears it up a little. And while this by no means covers every possibility or scenario I hope it helps in your games.