By using WiFi, your android device can connect to internet but normally it will be useless if the network is using proxy authentication. Anfroid Froyo 2.2 has option for proxy configuration (such as proxy address and port number) but it has no option for proxy username and password.
The trick is using TransProxy (abbreviation of Transparent Proxy). Before using this app you need to root your android device. I’ve tested some apps for examples Facebook, Market, Google YouTube, Google Sky Map, and they can connect easily through proxy with authentication.
To download TransProxy, simply click HERE (need to register first at XDA Developer forum)