Scott the logistics are fairly effortless. One can take an organised tour from the Peruvian city of Arequipa, however it's more fun and a little cheaper to do it solo. You take a local bus from Arequipa to a town around 40mins away from there the journey is interesting as you take a second bus for maybe around 2hours, but it's a fight to get a seat on the bus (no seats left, no problem sit on the floor! on and plays a hilarious and interesting ride.
When the 2 hour bus ride is over you spend the night in a small village type place at the top of the Canyon. The following day you fill up with supplies and head down.
At the bottom of the canyon accommodation is readily available for maybe no more than 4/5USD per night. In addition, the hostel down there put on dinner for around another 5USD.
If you decide to take the solo route then while you're at the bottom of the canyon 'grease up' a tour leader as he pull the shoots for a minibus ride back to Arequipa via a natural thermal spring and restaurant. The tour leader will charge probably a dollar or so more than going solo. And plus you'll get to meet people on the bus etc
Any question just ask.