This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
Benjamin, To test the servlet "for real", you need to deploy it to a server and test it. There are many Eclipse plugins for Tomcat - a free lightweight server. (Seach this forum for details.)
You also may be interested in writing automated tests. You can use JUnit to unit test the servlet passing it a mock request from easyMock/jMock. You can integration test the servlet on the server using Cactus or JWebUnit.