This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori 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.