The Sakai binary archive is available at http://source.sakaiproject.org/release/. The URL redirects to the most current release. If looking for an earlier release append the version number to the URL (e.g., http://source.sakaiproject.org/release/2.6.2).
Download the archive into $CATALINA_HOME and then unpack the archive. Then start up Tomcat by running the Tomcat start up script in $CATALINA_HOME/bin. Unix/Mac users should make sure that they have write permissions to the Tomcat servlet container files and directories before proceeding or start up permission errors may occur.
If you wish to configure a binary installation you'll need to manually create a /sakai folder in $CATALINA_HOME to hold your sakai.properties file.