The settings you will need will depend on the network you are connecting over. One big thing that will be needed: the network you are on can't have any sort of isolation on. Some wireless routers have a mode that isolates the wireless devices and won't route regular traffic to them; this is a protection feature, but it will also prevent AirDroid from working.
I can't be much more specific, unfortunately, since every router and network is different, configured differently, and calls this something different...and all of that assumes you have access to change the settings.
The easiest way to use it, or see if it works, is to load it and start it up, then type the address it gives you into your browser's address bar. You can use either one; the IP address will connect directly to your device, while the web address will go to their server and will route you to your device by the identifier code it gives you.
I highly recommend Chrome for this, as it is a very smooth experience and it supports everything AirDroid is doing. It should work fine in other browsers, too, though.
Basically, AirDroid works by acting like a web server on your device. Everything it does is something you can already do (technically speaking), it just gives you a web front end to do it in. That being said, it is an amazing project, and I hope it works out for you.