What is the version of Java that you are using for this project? (right click -> Build Path -> Configure Build Path -> Libraries). Javax.servlet is part of Java EE (enterprise edition) not Java SE (standard edition), so if you have something like J2SE-1.5, JavaSE-1.6 or JavaSE-1.7 it won't work. You need to download JavaEE-1.6 then go in Window -> Preferences -> Java -> Installed JRE and add the path of your newly installed version of Java. Finally, go back in the build path of your project and edit the JRE library used to select JavaEE-1.6.
If the project is targeting a valid server, the server should already be providing those libraries since it needs them to run itself. It's more likely that the project is either not targeting a server, or the chosen server is somehow not providing the basic Servlet APIs as libraries on the Java Build Path (and they should be coming from a server).