running power to my shed out the back, what's involved

The permanent version of this job is a submain: a dedicated cable from the main switchboard to a small board in the shed, with its own protection at both ends. It is licensed work, and the cable is sized for the distance as well as the load, because voltage drop over a long run is what makes a shed with lights that dim every time a saw starts.234

What drives the cost

• Underground versus overhead. Underground is tidier and usually preferred, but it means a trench at a compliant depth with marking tape, and rock or established roots make that slow.
• Distance, because the cable is a real cost and a longer run needs a larger conductor to hold voltage.
• Whether the main switchboard has a spare way and enough capacity, or needs work first.
• How much you want in the shed. Lights and a couple of general power outlets is a different job from a workshop with a welder.

Before anyone digs

Lodge a free enquiry with Before You Dig Australia and wait for the plans to come back. Water, gas, telecommunications and sometimes the electricity service itself run through suburban back yards at shallow depths, and striking one is both dangerous and expensive. The service is free and the response is usually quick.