Turpan is a small place by Chinese standards and is located right next to the main road.
It is easy enough to walk from the center to the highway (its around 5km). But still, if you feel too lazy then take the number 5 bus from the main square, next to the "three grape girls" monument. The bus will go a few zigzag turns around and its last stop is right next to the main highway and you can't ask for a better position to hitchhike east. Just don't forget that you have about 2000km of desert and mountain terrain in front of you, so be prepared.