You can go to your inbox and start a private conversation with them. Click on "Start a new Conversation" in the bottom right corner of the inbox pop-up, then enter the Mod's forums name, and write your message. Bam! Hope this helped

You can make an appeal here: http://www.skyblock.net/forums/net-appeals.192/
Make sure to click on "Post new Thread" on the bottom to start an appeal.
Make sure to follow the guidelines from here: http://www.skyblock.net/threads/ban-appeal-form-read-carefully.6/