Just create a thread on the meta board. Label it [Ban Appeal] for <insert original account name>.
From there explain you don't know why you were banned, include a link to your username. I believe your account should have also had a message from the Forum explaining that you were banned, with an email address to appeal to.
A couple things will happen, a random forum user will find the infraction. Most bans come down to plagiarism, and you would have to prove your account is a positive to the forum as a whole.
Usually it should not be how to do ban appeals, it should be that one should follow so that one will not get ban. As SOP for every organization/forum the respect to read the rules and regulations should always be the first thing to do as a user. This is why some don't pay attention to this and most of them committed violations and got ban reacted violently. They should be adhere their problems violently. LOL!