How about using Google for instance? There are thousands of tutorials and documentation out there. The most obvious being the one that you get when you click on the "Documentation" link in the upper toolbar of this page: http://udn.epicgames.com/Three/UDKProgrammingHome.html
Everything depends on your GameInfo class. It's the starting point for the other important stuff. It's referenced by the WorldInfo and can be accessed on the server with WorldInfo.Game.
The GameInfo defines in it's DefaultProperties the PlayerController, the AIController, the HUD, the GameReplicationInfo, the Pawn, the default inventory loadout and many other important classes from which it will spawn the respective instance when needed. So if you create a new gametype, you write a subclass of GameInfo and replace the references to UTPlayerController and so on with your own classes of that kind.
One way to make use of the scripts ingame would be with a menu like the one that comes with the demo content. But that's pretty unflexible and hard to edit for beginners, so you can just set in the WorldInfo properties of your map in the editor (accessible via F6 or the menu bar) the DefaultGametype to your custom GameInfo class and then the map will automatically be started with the gametype. There is also a system that assigns the gametype basing on the prefix of the mapname, which is controlled via the DefaultGame.ini and UDKGame.ini