Public support can help, but it's not enough to get a user unbanned, the mods have to have a clear reason before lifting a ban, such as;
• If a mistake was made, a user could have copied their own post on another website, which doesn't count as plagiarism
• The user is a net positive to the forum and probably did not break the rules for personal gain (was not on a bounty or signature), here a signature ban for a while could be issued.

An email address is usually included in a ban message. Send a mail to it, with your reasons why you should be unbanned.