Installation Alfresco requires Sun's Java Runtime Environment (JRE) or Java Development Kit (JDK) version 5 or later to be installed in order to run. Due to Java licensing issues, Linux distributors cannot currently include this software with their distributions and so this must be manually installed.
Depending on the flavour of GNU/Linux that you are running, you may be able to obtain the JRE or JDK via additional software repositories (which you may need to explicitly enable). Otherwise you can download binary installers for both the JRE and JDK from java.sun.com.
Despite the title of this document only the JRE is in fact needed in order to run Alfresco, although you will need the JDK if you intend to build Alfresco from source.