Very soon I was getting frustrated with it, because I could not start browsing internet without enabling mobile data connection (GPRS).
I spent two evenings frantically setting different kind of option/configuration variations with no luck. Finally, by typing the correct keywords to Google, I stumbled to Nokia forum where one poster had found out the correct settings to achieve browsing with wifi, without enabling mobile data connection.
See the original post here: http://discussions.nokia.com/t5/Software-Updates/Asha-302-Software-issue-told-by-nokia-care-Wifi-is-not-working/td-p/1349321
Apparently the instructions are valid for Nokia Asha 302, Nokia Asha 305, Nokia Asha 306 and most likely with Nokia Asha 311 too.
Edit 2013-03-30 added screenshots:
|1. Select "settings"|
|2. Select "configuration"|
|3. Select "web"|
|4. You can change to configuration name if you like|
|5. Go back and long press the menu button, then choose "activate".|
6. Set the Menu > Settings > Connectivity > Net Connection to "Ask first". Next time you open your browser it will ask you the connection to use.