This git repository helps you get up and running quickly w/ a tomcat installation on OpenShift.
Create an account at http://openshift.redhat.com/ , don't forget to create a namespace and install client tools as well.
Create a DIY application
rhc app create -a tomcat -t diy-0.1
Grab this quickstart codes and make it working for you!
cd tomcat
git remote add upstream -m master git://github.com/lulinqing/openshift-tomcat-quickstart.git
git pull -s recursive -X theirs upstream master
git push
That's it, you can now checkout your tomcat at:
http://tomcat-$yournamespace.rhcloud.com
The default managing account is tomcat/openshift