You can upload small WAR files to install them:
Login to the manager at http://localhost:8080/manager/html
Choose the file to install in the section labeled 'WAR file to deploy'.
Submit the file with the 'Deploy' button directly below the file chooser.
You can the access your application at the relative URI using the base name of the WAR file.
For example, myapp.war becomes http://localhost:8080/myapp/
WARNING: You really don't want to do this with large WAR files.