I decided to follow the advice of John Birmingham and Dirk Flinthart in their book "How To Be a Man". Not all the advice in the book is to be taken seriously (such as "How to land a jumbo jet"), but that on hair seems sound: when a gentleman's hair starts to thin, do not try and hide it; go for a very short haircut (Number 3 with the electric clippers).
But why pay $AU10 to have someone run a set of electric hair clippers over your head? So I bought a Remington hair cut kit for $AU14 from the supermarket. There are similar units on Amazon starting from $US11. The clippers come with a set of attached combs to set the hair length. These are numbered one to four and cut from 1/8 Inch for Number 1, to 1/2 Inch for Number 4 (the numbers seem to indicate the hair length in eights of an inch).
I went for the longest (Number 4) and following the instructions with the clippers: starting at the back, cutting upwards. Then I did the sides, similarly cutting up and then the front. I then changed to the Number 3 and did the back of my neck and sides, to create a slight layered effect.
The instructions say to remove the comb to trim the line across the back of the neck. There are many web sites saying how this should be shaped. Worried about creating a jagged line and taking chunks out of the hair, I found I could put one hand over the hair I wanted to keep on the back of the neck (with a thumb just under one ear lobe and foe finger under the other) and use this as a guide for the clippers.
A simple set of mains powered electric clippers seems the simplest. Replacement blades and combs seem to be readily available. If you have someone else doing the clipping, you might save some energy by using a manual set of clippers.
Sideburns were also an issue. But I wear glasses and found that putting them on created a guideline I could cut parallel to. Cutting your own hair is a hot topic of conversation on the web.
Cutting hair creates a mess. One proposed solution I am not sure about is the Fowbee, vacuum cleaner powered unit. If you are going to cut in the bathroom or outdoors, keep in mind that mains powered electric clippers should be kept away from wet areas for safety. A rechargeable battery operated set might be good alternative.