There are multiple hiking trails that lead to the ancient city of Machu Picchu: the Ancascocha Trail, the Salkantay Trail, the Lares Trek, etc. But the most popular of them all is the Inca Trail, and to hike it, you need a permit.
The Inca Trail is the traditional path that the Incas used to reach Machu Picchu in the 15th century, and it is the only route that will have you arrive directly to the Incan ruins on foot without having to take a train or bus in between.