Before installing stop blocks inside the bottom part of the chest, it goes without saying that the drawers must be complete and adjusted. If you have followed the same steps I have, you cut and planed the drawer fronts to size at the same time as you prepared the chest`s sides. All you have to do now is to cut and plane the drawer sides and backs.
All sides of my drawers are made out of maple. The fronts are about 3/4 in. thick, and all other sides are about 3/8 in. thick.
Once all pieces have been planed to the desired thickness, I cut a 1/4 in rabbet on all of them to be able to insert the masonite bottom.
Then, you may use your preferred jointing technique. Here, I have chosen to go with rabbets to make a strong joint.
What remains is to cut the piece of masonite to the appropriate size to make the bottom of the drawers. I then proceed with a dry assembly to check that everything is okay, and then glue and clamp both drawers.