With FHE the untrusted party can (usually) provide inputs (e.g. you can give them encryption of 1 and 0 that they can supply at some point in the circuit). But they cannot get _any_ non-encrypted output from the function without knowing the encryption keys (which would let them see everything).
FHE for secret operations is very straight forward. You first define a universal circuit— that is a circuit that can compute the result of any circuit (of the size) depending on its inputs. You then have the FHE environment run that universal circuit with the operations you really want specified as an input.
The result precluding blackbox obfuscation is really more about the formalism than a true practical impossibility, see Gentry's recent candidate indistinguishably obfuscation for NC circuts, which he boosts into full obfuscation for arbitrary circuts by implementing a pair of homorphic encryption decryption circuits under it.