When you downloaded Eclipse, did you choose the "Eclipse for Java EE Developer's" package? If not, go back and do that - that package contains WPT and various other packages helpful for building and running servlets.
I have one small quirk though..
Let's just say I'm trying a basic 'Dynamic Web Application' in Eclipse (I have the Java EE Developers' package installed), with a basic helloworld servlet like this : http://codepad.org/KzSB4m6z. Everytime, I need to put in the .CLASS that gets generated in the 'eclipse_workspace> proj_name > build > classes ' into 'eclipse_workspace> proj_name > WebContent' manually. Is there an automatic setting that does this ? I find that only by manually copying the .CLASS file to the location I mentioned does it work, otherwise it refuses to.
I'm using the local instance of Apache Tomcat from within Eclipse.