You should have Java 6 (or sometimes called Java 1.6) installed on your machine. For installing Java, you can visit the Oracle Java 6 download page and follow JDK Download and installation instructions.
IMPORTANT:
You should also set the environment variables like JAVA_HOME and PATH correctly. Then, download and install Tomcat 7 as described on the lab page.
You should also download and install Eclipse. Go to: http://www.eclipse.org/downloads/ and choose 'Eclipse IDE for Java EE Developers'.
Alternatively, if you do not want to mess up the Java installation on your machine, you can download CSE Ubuntu Virtual Machine and install Java and Tomcat on it. Note that this VM does not have a Java environment by default.