The GATK runs natively on most if not all flavors of UNIX, which includes MacOSX, Linux and BSD. It is possible to get it running on Windows using Cygwin, but we don't provide any support nor instructions for that.
The GATK is a Java-based program, so you'll need to have Java installed on your machine. The Java version should be at 1.6 (at this time we don't support 1.7). You can check what version you have by typing
java -version at the command line. This article has some more details about what to do if you don't have the right version. Note that at this time we only support the Sun/Oracle Java JDK; OpenJDK is not supported.
The GATK does not have a Graphical User Interface (GUI). You don't open it by clicking on the
.jar file; you have to use the Console (or Terminal) to input commands. If this is all new to you, we recommend you first learn about that and follow some online tutorials before trying to use the GATK. It's not difficult but you'll need to learn some jargon and get used to living without a mouse...