Hello Steve - welcome to the forums... thanks for joining!
When you are not connected to WIFI, you need to enable mobile data (3G) to be able to browse the web.
If, from your homescreen, you hit "menu=>settings=>wireless and network=>mobile networks" and then tick the "data connection" box and you should be good to go.
You might like to check androidforums.com/samsung-galaxy-s/ out, as this is where other SGS users hang out.
Hope the info above does sort you out and that you find this place a useful resource!! If you need any help getting around the forums, hit one of us guides up!