You send a forum PM (don't use IRC) to a TGNS admin (preferably the one who banned you, but any will do if not).

Tell him your SteamID, the playername you were using when you were banned, and any questions you have about the matter.

With rare exception, bans are issued on TGNS to players whom we hope to welcome back, but not until we've had a chance to have a one-on-one talk. It's one of the many ways we manage quality control on the server. Warns and kicks happen, but bans come swiftly to those who prove unable and/or unwilling to play within TGNS rules. Yes, some bans are permanent (typically repeat offenders), but most requests for re-entry are granted after simple discussion, as most folks who ever play here have what it takes to respect the server, its rules, and its playerbase, even if it takes a brief ban to realize how much so.

So, you're banned. Consider it an opportunity. Fire off a PM, and let's get things straightened out.