internet connection problems with the iphone 3
I've had this issue on my iPhone too after update to iOS6, I had to reset the network settings. This will clear all remembered WIFI networks and force you to connect to them again, creating new network settings. This means you will have to manually connect to your WIFI network again, and if required enter its password afterwards.

You can reset the network settings by selecting:

Settings -> General -> Reset -> Reset Network Settings

Also what can help is trying to clear the history of your Safari browser, you can do that by going to the Bookmarks -> History and then press the Clear button on the lower left hand corner of the screen.