The nights requirement for elite status are :

Silver- 10 nights
Gold - 50 nights
Platinum - 75 nights

You should be able to see how many nights you have this year by logging into your Marriott Rewards account. Status is earned on an annual basis. For initial qualification, Marriott also has an unlisted rolling calendar where you can move up in status if you hit the required nights for the past 52 week period. Updates to status by the rolling calendar occur every Monday.