The structure that directs protein synthesis in a cell is the ribosome. Ribosomes can be found either floating freely in the cytoplasm or attached to the endoplasmic reticulum. They read the sequences of messenger RNA (mRNA) and facilitate the assembly of amino acids into polypeptides, thereby synthesizing proteins according to the genetic instructions encoded in DNA. This process involves multiple stages, including initiation, elongation, and termination, highlighting the ribosome's crucial role in translating genetic information into functional proteins.