Attach the drawer slides according to the manufacturers instructions. The front of the drawer slides should be flush with the front of the divider.
Cut the drawer pieces to size and attach them together with 5/8" brad nails and wood glue.
Cut the drawer bottom to size and attach it to the bottom of the drawer frame with 3/4" staples and wood glue. Build 3 drawers.
Install the drawers with the drawer slides.
Measure and cut the drawer faces to size. Attach them to the front of the drawers with 1" pin nails and wood glue. There should be a 1/8" gap around all sides of the drawer faces.