Build large drawer boxes as shown. There should be 6 larger and 2 smaller. Check for square. Put your pocket holes in the front and the very back. The drawer fronts will cover the front pocket holes, and you won't ever see the back holes.
Build small drawer boxes.
Add drawer bottoms using glue and 5/8" finish nails. Both the small and large boxes are handled the same way.
Install drawer glides according to package directions allowing for a 3/4" inset to accommodate the drawer front. Working one drawer at a time, put the large drawer box in the dresser. Using 1/8" craft wood strips as spacers on all four sides, position drawer front and clamp. Attach using a few 1 1/4" nails. Don't put nails where your knobs will be be. I like to write in pencil where the drawer was originally fit (e.g. L4 for left side, 4th drawer down.) I found that the 1x8s I used varied slightly in width. (It's probably overkill, but I wanted to be extra cautious!)