connecting wifi module to proxy based wifi
First you need to understand the SOCKS protocol.

http://en.wikipedia.org/wiki/SOCKS

Then you need to implement that in your firmware.

Connecting the WiFi module to the access point is no different to any other access point.  Establishing the authentication, IP address, etc is all exactly as per normal.

The only change comes when you want to make a request to the internet.  Instead of making a direct request to the internet (say a HTTP "GET" request) you make a SOCKS request to the SOCKS proxy containing your request to the internet.