First they sew your T-shirts. Then they assemble your smartphones. Then they design your smartphones. Eventually, they will also design your T-shirts, other fashion and music.
This is what the U.S. did a hundred years ago, what Japan did 50 years ago, what China has done in recent years, and it's also what other formerly poor nations are going to do, if they are ever going to be formerly poor nations.
That also doesn't happen without some hickups in the nations that were formerly quite rich. Think of Argentina, for instance.
2- Why not aid? Bill Gates, someone who I'm not particularly fond of, claims it works: http://www.wsj.com/articles/SB100014240527023041494045793245...
Note I'm not necessarily advocating either of the above options. I'm just surprised at how persistent this belief in the properties of Free Trade is.