There's a nice, cheap used helmet on sale that is described as being 'large'. My head is 57cm, which is 'medium'. How well would this helmet fit (I guess it does vary between manufacturers), and how can I improve the fit if it doesn't?
I'd strongly advise against buying used helmets because you just don't know how well they've been looked after. If it's been dropped, it might be structurally compromised without your being able to see any damage. And, if you think about it, why would anybody sell a cycling helmet? I guess maybe if they've upgraded to something lighter and/or more aero but, in most cases, people will wear a helmet until they think it's worn enough that it needs to be replaced. If it's worn enough that the original owner doesn't want to wear it, you don't want to wear it either.
In any case, this one is too big for you. A circle with circumference 62cm has radius 9.9 cm and a circle with circumference 57cm has radius 9.1 cm. So, with the helmet centred on your head, you'd be able to move it roughly a centimetre in any direction.