In a low water year, like this year, pretty much all of the water lies on BLM ground. There is a large sign/kiosk along Blacks Creek Road that the BLM put up. It sits on their ground which is publicly accessible. If you park and walk from the sign, you will be legal. The upper portion of the reservoir that is currently dewatered sits of private ground. Traditionally, the landowners have allowed access. However, if they have it posted, you may not access it. There are no roads that access the north side of the reservoir. Access is only from the main Blacks Creek/Kuna road.
To ensure you know where you are, I would recommend buying a BLM land status map (Murphy map). It shows landownership in color. Alternatively, you can use the IDFG website's hunt planner or fish planner. There is a very useful map center from which you could view and print landownership maps.