If so, you will want to do a war deploy into that Tomcat - use the alfresco-war-1.2.1.zip file for that. (You will need to ensure that the MySQL connector is placed into tomcat/common/lib)
If you are not bothered about using your own Tomcat, use the alfresco-tomcat-1.2.1.tar.gz file or if you want to use Jboss Portal use the alfresco-jboss-1.2.1.tar.gz file. (Untar these to where ever you like, e.g. following the 'Install Alfresco Tomcat Bundle' section of the README to /opt/alfresco, then follow the 'Create Database' section of the README. Optionally install OpenOffice if it is not already installed [this is recommended], then follow the 'Running the Alfresco Server' section of the README).
If you want everything done for you, use the full 'everything you need' bitrock install that contains pre-configured MySQL, OpenOffice, JDK, Tomcat and Alfresco - alfresco-1.2.1-linux-community.bin. (see here for install info: http://wiki.alfresco.com/wiki/Linux_Quik_install)