IMPORTANT UPDATE INFORMATION (Nov. 2021): To all who want to Visit Torres del Paine National Park you may visit the official book site Booking Patagonia at: www.bookingpatagonia.travel
In order to visit Torres del Paine National Park, you need to purchase an entrance ticket. Now you may buy it online by visiting this link: https://www.aspticket.cl
Remember that you need also reservations for the campsites or shelters in Torres del Paine.
There are three different agencies (CONAF, Vertice, Fantástico Sur) that offer campsites and shelters in Torres del Paine National Park. The campsites you need to reserve will depend on your route and budget.
I recommend trying to make reservations at the same time since the three agencies are not connected, which makes it very difficult to coordinate them.