Unfortunately, most Linux distributions do not ship with Java due to its license fee. Certain Java implementations are free, such as GCJ, or the GNU Compiler for Java, but it isn't Sun's Java implementation, which is arguably the better of the two.
Luckily, installing Java on your Linux system is extremely simple. Visit the Java download Web site and select the operating system you'd like to download for (Linux, Linux AMD64, Solaris, etc.). Once you've chosen the download file--either a self-extracting executable or a self-extracting RPM file--you can install it. In this case, the latest version is version 5.0 Update 5 and uses the self-extracting binary:
# mkdir -p /usr/local/java
# cd /usr/local/java
# mv /path/to/jre-1_5_0_05-linux-amd64.bin .
# chmod u+x jre-1_5_0_05-linux-amd64.bin
The installation must be done as root if you want the Java installation to be site-wide; if you want it just for yourself, you can extract the package in ~/bin/java or some other appropriate location. In the above, the JRE is installed in /usr/local/java/jre1.5.0_05/.
As a quick test, run the java executable:
# cd jre1.5.0_05/bin
# ./java -version
To make Java available to all users, add it to the default PATH settings by editing /etc/profile and adding:
export $PATH $JAVA_HOME