how do I block caller id on an iphone 4s?

Settings/Phone/Show My Caller ID

turn that off

Settings/Phone/show My Caller ID/ .....does not exist on my new 4S

That setting only exists on GSM iPhones, if you have a CDMA phone on Verizon, as an example, you won't have that setting. Also, some carriers do not permit turning caller ID off, and if your carrier is one of them, that setting will not appear.

I'm not sure if this works across all carriers, and it's probably limited to U.S. carriers, but for what it's worth:

If you dial *67 before the area code and phone number, that should block your caller ID for this (one) call.

So, for example, if you were calling (987) 654-3210, you would dial: *679876543210