A lot of onions put on top growth until June 21st and then when the year turns (days start getting shorter) they concentrate on making bulbs - so the bigger the plants grow this side of June the better as they can make bigger bulbs. Overwintered onions behave a little different - but not much.
As the bulbs are reaching their maximum size the tops start going brown and will fold over an inch or two above the bulb - after this they won't get any bigger. Bulbs with thick necks or going to seed wont do this and you should eat these first as they won't keep for long.
A lot of people then lever them up with a fork, shake off the soil and lay them on the soil with the root end facing the sun - this is said to ripen them so they store better.
Of course if it happens to be raining you will be better keeping them somewhere dry (greenhouse) to do this. When they are completely dry (the outer layer should be paper dry). Store them somewher cool and dry.
I did this last year and I still have some left in the garage.