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.
In Eclipse, you can import a project directly from a ZIP file: select File / Import, then choose General / Existing Projects into Workspace. Then click Next, select "Select archive file" and click the Browse button to select your ZIP file. Then click Finish to import the project.
Note: If the ZIP file already contains an Eclipse project, you do not need to create a project manually first.
Have you defined your Tomcat installation as a server in Eclipse? Go to Window / Preferences, then select Server / Installed Runtimes. If your Tomcat is not yet defined as a server, click the Add button and add your Tomcat as a server.
If it still doesn't work, then check if the versions are correct. Was the project made for the same (or a compatible) version of Tomcat and Java as what you are using?
Note: Since this question is more about how Eclipse works than about Tomcat, I will move it to the IDE forum.
Please refrain from using words such as "Urgent!" when posting. Your question is no more and no less important than anyone else's. In fact, by using the such terms, you you can delay or prevent useful response to your question. Please read this to find out why.