You can see the size of a unit when you place it in an editor, it's the green box.
If you want to know the size in pixels you can just take a screen shot, paste it into an imaging program, and count it that way.
Here we see the scourge. It is 24x24 pixels.
The unit is snapped to the grid. Its center pixel is where the grid lines meet.
For some units, the center isn't even near the center of the unit, such as in the case of the Dark Templar. You can see that the grid lines meet way up near the top of the unit.