More specifically...
Challenging:
1) You log into the ACC
2) You use the "challenge" [not "challenges"] link in the left menu
3) Select an opponent from the scroll-down menu (if you are below the ACC rank of Seeker, you might only see the Operators as an option for opponents. That's because you have to qualify before you can fight the rest of the B-Hood. Training fights are also available in that case to get you practice before the Qualification)
4) Select a Hall (different Halls are used for different things, but the "Combat Centre" is the main, standard Hall)
5) List your weapons; it should go without saying that (unless fighting in the Jesters Keep), you should select the weapons you actually have skill in
6) Submit the challenge and wait for your opponent to accept
ACC Gaming:
These are stories about fighting. Much like a JK/JO/JA/XvT/XWA/SWBF battle, no, your character doesn't actually die... if that were the case, there's a few ACC-ers that might be on like their 17th character
As Nekura said, the fiction behind the battles is the Morph Hall, a computer generated enviornment that simulates everything... including death of a combatant.
Unlike video games, these battles are written - but that is really where the differences end. Like video games, in the ACC you can only use what you have (notwithstanding things like sticks and rocks if you chose to fight in a forest, for example), you can only accomplish what your character is capable of doing at the time and you can't create things that weren't there when you started to try and gain an advantage.
Dying:
No. You don't always have to die. Yet, as Nekura mentioned, REALISM is a part of how the battles are rated (and that's realism as it applies to this fictional environment). So, you're a Hunter... if you were pit against a Pontifex/Overlord/Primarch there's little chance that you would survive in the 'realism' end of it.
HOWEVER...
.:THE TWO WINS OF AN ACC BATTLE:.
There are 2 different wins, or victory's, that are part of the ACC process... and only ONE of them matters. One victory is within the story, where you kill your opponent. The other is when the battle is rated and a winner is chosen. *Because you kill your opponent, within the body of the battle/story, DOES NOT mean you automatically win the fight. The Judge rates the battle based on the content and some criteria, or personal preference... from that, the combatant who stayed true to their character, wrote better and kept with the story's realism and continuity will be selected as the winner. IT MAKES NO DIFFERENCE IF THEY DIED WITHIN THE BATTLE'S TEXT.
And that is the only victory that matters... your selection by a judge as the winner, NOT what is written in the battle.
Hope that cleared some stuff up for you.