Glycolysis has two phases - preparatory and pay off. Oxidation of glyceraldehyde 3-phosphate to 1,3-biphosphoglycerate takes place during pay off (energy conserving) phase.
In the presence of enzyme glyceraldehyde 3-phosphate dehydrogenase, glyceraldehyde 3-phosphate is oxidised through removal of hydrogen and addition of phosphate from inorganic source to form 1,3-biphosphoglycerate. NAD+ is hydrogen acceptor. It produces NADH.