You can deploy a new WAR file to your Tomcat server. To do this navigate to the desired Virtual Host resource for that server. On the Inventory tab you should see a "Create New" drop down. Try that out.
Once a WAR is in inventory you can navigate to its Content tab and from there perform updates to new versions etc.
The tricky thing here is that new resources are always created from the *parent*'s Inventory tab and content management of an existing resource is done
via the Content tab.
Also, check out 
Hope this helps.