It is very easy to find.
Head west from Alice on Larapinta Drive then 50ks out onto the Namatjira Drive turnoff. Then about 5-10ks along there is a turnoff right where the Namatjira crosses the Hugh River. Track is only 15km to Birthday Waterhole and another 7km into Hugh Gorge.
I don't think the waterhole will be this nice in a few months though. We have had exceptional rainfall over summer but they do drop pretty quickly once the flows stop. Still a great trip with some excellent hikes in the area.