This is probably one of the easiest home DIY jobs you can get. Shower head leaking at one of the joints in the head or piping from the wall. A brand new shower head is $15ish from Stratco. I was in there today, but that will be another story. Btw, I think the same shower head was $20ish from Bunnings, so it does pay to keep your eyes open. You could try (and I did) to repair the leaks, but the little “o” rings that are in each joint are very difficult to match perfectly and thread tape just won’t last, so at $15ish just buy another one and whack it in (carefully!).
First, you dont have to turn off the water mains because the water only gets to the shower head if you turn one of the taps on. Just grab a large wrench and undo it. Clean up the thread, replace some new thread tape and fit the backing plate, which just slides, sits in place. I had to re-use the old backing plate as the new one sat a little too high and left no thread to attach the new head. It polished up perfectly, but another reason not to let these things go too long without fixing them. If I’d left this another couple of months there could have been rust on the plate and/or in the thread caused by the leaking shower head. To make sure you don’t scratch your new shower head I used a tissue to protect it from the wrench. You dont need to tighten it excessively, just pinch it up snugly to the thread tape, then adjust the head swivel points to get the right height and angle, test, and you’re done.