The description in the Derby Server and Administration Guide regarding how to operate the Derby Network Server using the servlet interface is a bit terse, so this page offers some additional guidance about how to get this feature to work.
Thomas Hill was successful using the following steps:
Deploying the war file into tomcat using the tomcat manager application placed the war file 'derby.war' into tomcat's webapps folder (/var/lib/tomcat5.5/webapps/ on my debian system) and also created a folder within webapps called 'derby'. Initially the derby folder created only contained one subfolder 'WEB-INF' in which only one file 'web.xml' was found.
Within the WEB-INF folder I then manually created an additional folder 'lib' into which I placed 'derby.jar', 'derbynet.jar' and 'derbytools.jar'. (Note: I made user 'tomcat55' the owner of the folders created and of all derby jar files which I copied over, and specified 'nogroup' as group. (so I actually did not need to place anything in ../common/lib).
Restarting Tomcat and then opening URL http://localhost:8080/derby/derbynet returned a screen confirming that the 'Derby Network Server has been started' and the screen also offers some buttons, e.g. one 'Stop' button which can be used to stop the server again.
The last thing I did was to add line derby.system.home=/var/lib/derby/derbydata as the last entry in file 'catalina.properties' (found under /usr/share/tomcat5.5/conf) so that database files are created and stored in a separate location and not within the tomcat hierarchy.