Once I had the EE version of eclipse i set out to make sure that EGit was installed and configured. It was already installed out of the box. So I cloned my project and then imported it into eclipse as a maven project. All this was done by following these instructions.
Once that project was in my eclipse I built it by right clicking on the project -> Run As->Maven Clean. Then right clicking on the project -> Run As->Maven install.
This kicks out a open.war to webapps/target folder. Then I deploy the openmrs.war to webapps folder in tomcat and am able to access the site via localhost:8080/openmrs.