It depends what sort of headset you have. The size of the steerer tube is not what differentiates the two designs.
A "normal" headset uses a steerer tube which has a thread cut into it, and which only just sticks out of the top of the frame. These headsets use two great big nuts above the top part of the headset which screw onto the steerer tube to hold it all together. Then the stem has a wedge which sits inside the steerer tube to hold it in place.
An aheadset uses a non-threaded steerer tube which sticks a couple of inches out above the frame. In this case the headset is just slotted into the frame and the stem tightens down onto the steerer tube to hold it all in place. This is preferred these days because it's lighter and doesn't need huge spanners to tighten it up.
As for fitting headsets, the usualy recommendation is to find a nice shop to do it, it's tricky because they usually fit very tight and fitting or removing them normally involves the use of a mallet!