All levels are based on nights as far as I understand. There is no points meter in place to qualify for Silver, Gold, Platinum, and/or Platinum Premier.
Short and sweet:
Silver needs 10 nights
Gold needs 50 nights
Platinum needs 75 nights
There are "challenges", credit card nights, and roll over nights to help achieve these targets.
At Marriott.com there is a link for Marriott Rewards. Scroll to the bottom and there is a link to "Elite membership" under Terms and Conditions for more official info.