When you leave HIFS you make a right out of parking lot (by the lobby) go to the 1st light by Gaylord Palms Hotel (can't miss it, it is a huge place) make a right and that road takes you to WDW from there you follow signs to MK. From what I remember you go right to the booths where you pay for parkng at MK (however you will not have to pay) Just tell the CM that you going to the Contemporary, he will direct you to go over to the right, there is a sign MK resorts and you will follow signs to Contemporary. It is really very easy. On our recent trip we did this a few times. It was leaving WDW that we always seemed to get lost. Just remember when coming back to HIFS if your not sure where to go look for the tall tower of the Marriott World Center or Gaylord Palms. They are so big you can see them from quite far away.
Also, FYI if you go out of the parking lot as above and straight through the light at Gaylord Palms, that road will end at rt 192. Where there is a Publix grocery store, a Walgreens, and countless restaurants.