Connect your garden hose to a hose drill. Other tools such as power washers may work as well, but the hose drill is a tool that's specifically meant to cycle up water pressure from your garden hose to turn it into a digging tool.
Open up the water pressure and turn on the hose drill. Hold the drill with both hands above the section of the earth you want to dig a hole in and press the button to release the stream.
Continue holding the button, giving occasional pauses to check the progress of the hole. Once you're satisfied with the depth of the hole, turn the hose drill off, and shut off the water pressure. Drain the remaining water out of the hose drill by tilting it on its side and pouring out the water that wasn't used.