This is our first visit to Mesa Verde NP, so going on ranger guided tours of the main features is a good way to start. We did a morning tour of Balcony House, then an evening "twilight" tour of Cliff Palace, and finally a morning tour of Long House. We also did driving around and walking out to viewpoints to see other areas in the park.
BTW: I would highly recommend the Spruce Tree Terrace cafe near the Chapin Mesa Archeological Museum as a great place to eat. Their BBQ options are smoked right there and are delicious!