What triggers DNA to produce proteins?
This question is not easily answered as there are a multitude of factors involved in the production of proteins.  DNA - the molecule - does not "determine" when proteins will be produced.  The environment (truly environmental, extracellular, intracellular, etc.) of the organism governs this.  If you have not found enough material to satisfy your inquiries I recommend Jim Watson et. al. Molecular Biology of the Gene.  A classic.