In order to earn Starwood Platinum status you need to make 25 stays or spend 50 nights per year at Starwood properties. If you have the Starwood American Express credit card you automatically get five free nights and two free stays towards elite qualification annually.
As a Platinum member you earn two base points per dollar, plus a 50% bonus for being a Platinum, for a total of three points per dollar spent.
As far as on-property benefits go, Starwood offers free internet at all their properties worldwide. Furthermore, you get access to the club lounge at those properties that have lounges (though I find Starwood hotels to proportionally have far fewer lounges than the other chains). The main draw for people to the Starwood program seems to be the lure of free suite upgrades. They offer Platinum members the best room available, including standard suites.