You can use it with Apache or by itself. Somewhere within the many config files you can configure the ports and protocols that it will listen on and for. Default is probably http on port 8080. If you don't need apache, you can just use this, or switch it to port 80. To integrate with Apache you could either do http proxying (apache just forwards requests on port 80 to tomcat on port 8080) or a custom protocol between the two: ajp. Google that for configuration details. I believe you'll need mod_ajp for apache. At any rate, in both cases, Apache would be a front end to tomcat.
It's been a while since I've installed a war into tomcat but you should be able to drop it into the webapps directory. You might have to edit a tomcat config file somewhere to give it a specific path (I'm going totally on memory here instead of actually trying it out

). There's a manager application installed in tomcat by default but you have to enable an account to be able to access it. I think it's at /manager, but the default install page will tell you.
But heck, why am I explaining all this? If your dev knows how to use it on window, he knows how to use it on linux. It's the exact same layout but the startup/shutdown scripts are .sh instead of .bat. I would strongly suggest you visit the tomcat website and at least dip into the documentation a little bit.