you compile and run them the same way as on windows, however youll need to install the Java JDK (just like you have to on windows).
go
here and download the first item, 'JDK 6u1'
since your on fedora, you can download the RPM, which is under the heading 'Linux Platform - Java(TM) SE Development Kit 6 Update 1', and filename 'jdk-6u1-linux-i586-rpm.bin'
to isntall the RPM read the
instructions.
to then compile and run programs with simply 'javac file.java' and 'java file', respectively, you have to have the path to the 'javac' and 'java' binaries in your PATH variable. search here or elsewhere for how to do this, as it is very common.
to find out where these files are located so you know what path to add, use a find utility (either command line based or from your GUI) to search for files of name 'java' or 'javac'. they should both be in the same directory.
regarding gij ive never heard of it.