That's a really good question. I can answer part of it. I can answer the how they get the crane there part and the why isn't the country littered with cranes part.
The crane is dismantled by a professional from wherever it was before its use was requested at the site. Once dismantled, it goes on several trucks, including flatbeds, stepdecks, and RGNs (removeable goosenecks in case you were wondering) to be delivered to the work site. Depending on the size of the crane, it can take up to 65 trucks to get the entire crane to the site!
The country is not littered with cranes because they are very valuable and often rented by the hour. It can cost up to $1,500 per hour (or more in extreme circumstances) just to have a crane onsite and ready to operate. Once the current lessee (or sometimes owner) is done with the crane, they are eager to ship it on to the next place where it will be put to use, or at least no longer be charged to them.
Hope that helped. I'm in heavy hauling and shipping, so I've got some experience here. :-)