How does RNA transcription determine which half of the DNA to use?
I'll keep this short and simple. The direction of transcription (which determines which strand is used as the template) is controlled by the promoter, which is a region of specific DNA motifs at the 5' end of a gene. RNA polymerase binds to the promoter, which orients it on the correct strand and in the correct direction, after which it can proceed to transcribe the gene. 



That great little animation is from this website.