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.
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