earroway,
You can export a project as a WAR file using File > Export > MyEclipse JEE > WAR file > Select the project to be exported, browse the destination and click Finish.
Once the WAR file is created in the selected destination, place the WAR file under Tomcat webapps directory and restart Tomcat. A folder with project name will be created and you can find all the libraries under <Tomcat dir>\webapps\ProjectName\WEB-INF\lib folder.
Hope this helps and let us know if you see any issues in MyEclipse.