First you need a JDK from Sun, the JDK that comes with most Linux distros is inadequate to run an app server. Download from http://java.sun.com/javase/downloads/index_jdk5.jsp, install it, and then set JAVA_HOME. I set mine as follows:

export JAVA_HOME=/opt/java/jdk1.5.0_13

For the Jboss App Server, download the 4.2.1.GA zip file from http://labs.jboss.com/jbossas/downloads/, unzip it somewhere (I unzipped mine such that the installation directory is /opt/jboss/jboss-4.2.1.GA).

Installation is now complete. To run:

cd /opt/jboss/jboss-4.2.1.GA/bin
./run.sh

To access it, point your browser to: http://localhost:8080