Purchase a plane ticket from Santiago to Punta Arenas.
Arrive at the Santiago airport a few hours before takeoff to allow yourself plenty of time to check bags, go through security and find the proper gate.
Arrive at Punta Arenas.
Hail a taxi. Tell the driver to take you to the bus station.
Arrive at the bus station.
Purchase two sets of tickets. One from Punta Arenas to Puerto Natales, the other from Puerto Natales to Torres Del Paine.
Board bus from Punta Arenas for Puerto Natales.
Arrive at Puerto Natales.
Board bus from Puerto Natales to Torres Del Paine.
Arrive at Torres Del Paine.