Hi there, Breck!
The only tram service Walt Disney World provides is from the parking lot of each theme Park to the Park itself -- or, in the case of Magic Kingdom, to the Transportation and Ticket Center, which is where you'll catch either a monorail or a ferry to the Kingdom.
If you are not renting a car, you'll be relying on the
internal motorcoach transportation, provided at no charge by Walt Disney World.
To get to Disney's Contemporary Resort from Disney's Wilderness Lodge, you will need to take a bus to Magic Kingdom. From the bus stop, the walk to the Contemporary will take just a few minutes; there's a path leading directly to the Resort. Give yourself 45 minutes to an hour for the journey.
Epcot is a slightly easier prospect. There's a bus from your Resort to every Park, and it'll take you directly to the entrance. Give yourself 45 minutes for that, too.
The times I've offered will provide you with a little padding in care you have a reservation to keep.
Have a wonderful trip!
See you later, celebrator,
-Deborah B.