The simplest method is to catch the train (Peru Rail) directly out of Cuzco. You should plan about (4) hours total for the train ride. If you chose the train out of Cuzco, be sure to purchase your ticket in advance. I was there in the off season, and the actual days that I wanted to travel were sold out. There are several classes of service available. The cheapest, which is what I took, is known as the Backpacker train. It costs $96 US for a roundtrip ticket. My only complaint regarding the Backpacker train was that there was no leg room available. My knees actually interlocked with the passenger across from me, as you sit facing one another. The mid priced train, known as the Vistadome appeared to be much nicer, and looked to have a bit more room. The fare for the Vistadome train is $142 US for a roundtrip ticket. The most expensive train, which I happened to see as it passed by, looks to be pretty luxurious. I was told that it is $500 US roundtrip, but that is second hand information only.
The train will drop you off at the train station in Aquas Caliente. If you were to immediately climb Putucusi, all you would have to do is walk along the railroad tracks (continuing in the same direction) until you reach the edge of town. Right at the very last building (which is under construction at the time of this writing), look to your right and you'll see the trailhead, partially hidden under dense brush, but visible if you're actually looking in the right spot. I missed it because I was told that it was a (10) minute walk from town and that there was a sign marking the trailhead, both of which were not the case. So, if you come across any tunnels or a switching station, you've gone too far.
Once you're on the trail, it's impossible to get lost. The trail basically goes straight up the side of a steep mountain. As I recall, I made it to the top in about an hour, maybe a little more.
Red TapeNo red tape or permits required. Climb whenever you want.
Camping - Hostals - HotelsI saw campsites below town along the Urubamba River but I didn't camp here. I did talk with one backpacker that was simply camping along the bus road between Aquas Caliente and Machu Picchu.
I preferred the hostals, which are literally everywhere in Aquas Caliente. I paid about $7 US for a private room with a shower (& hot water most of the time). I was actually met at the bus station by several hostal owners trying to convince me to stay at their place (same thing happened at the bus station in Cuzco). Prices were definitely negotiable, so I'd take my time and check a few out before commiting to any particular hostal.
There are also plenty of hotels around town as well. And then there's the lodge at Machu Picchu for those with the money. The cheapest room starts at $795 US per night, and tops out for a suite at $1,320 US per night. I've added a link for those that care to check it out.
Machu Picchu Lodge
Weather LinkCurrent Weather Forecast
LinksLots of good information on this link to get yourself familiar with the train service.
Information from Wikipedia on Putucusi.
More good information from Wikipedia on Machu Picchu on this link.
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