You don't once it's been banned it is gone forever.
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If you are asking how to unblock an account that has been blocked, you can't. You either wait for the ban time to expire (If it was not perma banned) or send a email to the mods.
You might be able to get your account back after being banned from AirG but it is totally up to the operators. You can try writing a letter or complaning to the account representatives, but there is no simple solution for getting your account back.
You have to link your Dragonfable Dragon Amulet account to your AQWorlds account.
If your account was permanently banned, there is no getting back on. You will have to start over, and too avoid getting banned, do not break the rules of RuneScape.
If your account was stolen, hacked, banned or payment issues, you will have to contact Player Support team in order to get your account back.