Occasionally, you'll have the opportunity to enter tournaments to win Cards and Gran. All Tournament activity happens in a separate arena you can reach from the Game Tab, either using the Hexagonal menu or the button on Game Home.
When you enter the Tournament Lobby, you'll see a list of active Tournaments. Click on one, and it'll give you the option to enter if you're registered, or to register if you're not. When you first register, you'll immediately be taken to a Sealed Card File select screen, where you pick a Card File and hit OK. Generally, the Card Files are all random so it doesn't matter what you pick, but if it's different you can find out by reading the Tournament Rules on the Alteil main site.
After you select a Sealed Deck, you'll be brought to a Card File editor, where your tournament cards (and only your tournament cards) will be displayed. Here you can put together a Card File, but don't sweat the details, you can always come back here and edit it again.
Once you save your Card File and exit, you'll be taken to the Tournament Arena. Here you can duel, look over your statistics or check the rules of the tournament. There are also buttons for exiting and editing your Card File. When you go to the Card File editor from within a Tournament, it will not take you to your Tournament Card File only, not your main account Files.
Different Tournaments have different rules, but the standard tournament runs like an Arena, where you fight random duels and try to get a number of wins in a specific time. In a win % tournament, there is a minimum number of duels to qualify, and once you reach that you can choose if you want to endanger your win % by fighting more. However, your battle record is the tie-breaker, so an 11-0 record beats a 10-0 record. As a further tie-breaker, in case of identical record, whoever duels last wins. In a Star Tournament, everyone starts with 5 stars. If you win, you take one of your opponent's stars. The highest number of stars wins, with your win % as a tie-breaker. Star Tournaments encourage more duels per Iczer, and remove the possibility of a single loss destroying your record for good. However, if the longer they go on, the more they cater to "grinding".
These vary by Tournament. Free or Fight Money Tournaments usually have minor prizes, while Gran tournaments have better prizes. Prizes will be listed on the main web site when a Tournament is ongoing.