Most tourists visit Colca Canyon with a guide or as part of a tour group, but it is fairly simple to do independently. Visiting on your own gives you more flexibility with which sites you want to see and how much of your time you want to spend on trekking. Here's the "how to" breakdown and cost of how we did our trip. Bus from Arequipa to Chivay (4 hours, S/12, $4.59 each) - Busses leave from Terminal Terrestre, and it is recommended to buy tickets a day ahead to ensure you have a seat. Our bus was over an hour late, so don't plan to go too late in the day.
Spend the night in Chivay. We stayed in a private room with bathroom at a random hospedaje just outside the plaza area (S/30, $11.48).
Catch the 7:30am bus from Chivay to Cabanaconde (2 hours, S/4, $1.53 each). Arrive at the bus station and get in line immediately, even if there is nobody else standing there if you want a chance at getting a seat. The bus will be crammed full with people bursting out of the aisles for the entire duration. Someone in a green vest will board the bus to sell tourists their ticket into the canyon (S/70, $26.79 each). You have to buy it, and they check that you have it at various points along your trek.
Get off the bus at Cruz del Condor. You can't miss it, as it will be the first major stop where a lot of people get off. They say at the bus station that it takes only one hour, but it is actually almost two. Walk around and take lots of pictures of the condors and take in the views of the canyon.
Walk to Cabanaconde along the road. It is 12km and took us around 3 hours with our bags. It is a beautiful walk without many cars and the road is in great condition. Once you get there, immediately buy your return bus ticket to Arequipa, if you want to have a seat during the seven hour journey (S/12, $4.50 each). Note: The cost of the ticket is more if you wait until you are on the bus to buy it.
Spend the night in Cabanoconde. We stayed in a private room at Pachamama (S/50, $19). They have a decent restaurant which serves wood fired pizzas, and breakfast is included in the cost. The staff are very helpful and give lots of good tips on where to go and how to get there.
Trek from Cabanaconde to San Juan de Chuccho (about 3.5 hours, mostly downhill). Bring plenty of water and snacks, as both are very expensive once you are down into the canyon. Once you cross the bridge at the bottom, follow the signs painted on rocks for "Roy", and eat a wonderful lunch. Spend the night in a private room with a gorgeous view of the mountains. (Lunch and dinner: S/10, $3.83 each, Breakfast: S/6, $2.30 each, Lodging: S/20, $7.66 each)
Trek from San Juan de Chuccho to Sangalle el Oasis. Brush up on your Spanish to ask locals for directions when you inevitably take a wrong turn, as there are no signs anywhere. It is supposed to take 4 hours, but took us a little over five with our "detours". There is a good mix of up and downhill.
Spend the night in Sangalle. We didn't like it at all, but many people do. All of the "resorts" are similarly priced at between S/10-15, $3.83-$5.74 per person, with meals being S/10, $3.83. Make sure you bring your bathing suit and headlamp, as there are swimming pools, but no electricity. Also, if you have one, bring a silk sleep sack. The bed sheets are very rarely changed.
Make your ascent from Sangalle back into Cabanaconde. It is best to leave early in the morning, because it gets very hot with little shade in the late morning and early afternoon. It is a very demanding climb, so be prepared!
Spend the night in Cabanaconde (S/40, $15.31), and take your return bus to Arequipa the following morning. Make sure you bring snacks and use the restroom before you go... the journey is around 7 hours with no bathroom breaks!
There are many other routes that you can take, from single day trips to multiday hikes. The nice thing about the canyon is that you don't have to camp if you don't want to. Water was one of our largest expenses, because you need a lot of it and it was relatively expensive at S/10, $3.83 for a large bottle in the canyon. Make sure to bring small bills, because the locals are mostly unable to make change. Also, sunblock and a hat are a must!