Before looking for support, be sure to read the available documentation, whether that is the application handbook, developer documentation or other. Look at the boxes to the right for resources for Kate, KWrite and KatePart.
When in need for support, you have the following options to get in touch with Kate developers and users:
Many of the bigger applications using KatePart such as KDevelop, Quanta etc. have their own support channels, mail lists, irc channels and web forums. If you have a problem with one of these applications and you are not sure if this is a bug of the KatePart then first report it to them.
The KDE bugzilla at http://bugs.kde.org is used for managing all bugs related to kate. You can use the Help->Report Bug menu item found in most KDE applications to report bugs or wishes. It will start the bug report wizard and fill in some information for you.
Be sure to include as much information as possible when reporting bugs, the better the report the better the chances we can fix the reported problem.