It took me a while to find the answer to this, so I'll blog it here. Maybe this is just me not being familiar enough with this kind of thing, but there was no cover to slide, and I couldn't find the right hole to poke!
Holding the phone as if you were looking at the screen, turn it over so you're looking at the back. On the end near you there is a tiny round hole and a long narrow slit where the plastic back battery cover meets the metal frame that holds the screen. Ignore the tiny hole. Put your thumbnail in the slit, then force the cover off. Don't worry, you won't break it. It comes off pretty easily once you have that leverage.
Here's how I found out how to do it - but ironically, this is not my phone model.
Mine is a T-Mobile, Android like all Galaxys, but it doesn't say on the device what its proper name is (Vibrant). Galaxy S apparently also comes in Fascinate and Captivate or something like that, and one has a sliding cover, so it gets confusing. Hope I am able to help someone here.