The following assumes you're using a dedicated Tomcat instance to run Artifactory and that you've used their $ARTIFACTORY_HOME/bin/tomcat-install.sh script to do a standard installation, so that Artifactory is listening on http://yourhost.yourdomain:8081/artifactory, with an AJP listener on port 8019.
sudo a2enmod proxy_ajp
Set up the Apache site configuration to proxy requests to Artifactory - default config file under Ubuntu is /etc/apache2/sites-enabled/000-default
ProxyPass / ajp://localhost:8019/artifactory/
ProxyPassReverse / http://yourhost.yourdomain/artifactory
ProxyPassReverseCookiePath /artifactory/ /
Add these lines just before the end of the VirtualHost section.
sudo service apache2 restart
Now Artifactory should respond on http://yourhost.yourdomain
Finally, go to the Admin tab in Artifactory, select General in the left toolbar and set the Custom URL Base field to http://yourhost.yourdomain