Scrambling eggs requires fine judgement. You have to catch them at the moment when they are no longer runny but before the curds set and harden. The curds should be fluffy, holding the liquid content in suspension.
It is easier to spot the arrival of this state if you cook the eggs in a (non-stick) frying pan, I have found. It is certainly a good idea to avoid using a saucepan with a small base, which will not allow you to heat the egg evenly, no matter how thoroughly you stir. Of course, you could try using a larger saucepan. But I think that the gentler stirring that the frying pan encourages (so that the egg does not slop over the side) produces a better result, because overbeating results in a less pleasing, porridgy texture. The process is rather like cooking an omelette, only continuing the first stage (stirring, and pushing the set egg around to give the rest access to the base of the pan) throughout.
I admit that I've bumped up the contrast on this picture. But these eggs, which come from Nantclyd Organics, really are very rich and yellow.
Scrambled egg recipe here.