If you are going by PT, catch any of the buses that depart from stand C (I think, maybe it is B) in Eddy Ave at Central, on the side that the park is on. The buses arrive really frequently.
Buses such as 372, 393, 395 + more (there are HEAPS) all travel right near Fox Studios, either down the Moore Park bus lane or on to Anzac Parade. Just ask the driver where to get off, and it is a really short walk to Fox Studios.
Use the trip planner at transport info.