With the drawer in place, test that the drawer support shelf fits tightly between the sides of the night table case. Sand the edges if necessary to get a better fit.
Apply a small bead of glue to the back and side edges of the support strip and glue it in place below the drawer, taking care that you don't push the drawer too tightly against the top of the case. Check that the support lines up with the marks you made earlier on the sides of the case. You want to make sure it is inserted squarely into the case and doesn't angle up or down against the base of the drawer. Clamp the support in place and leave to dry. You may want to pull the drawer out of the case slightly in order to make sure any extra glue doesn't glue the drawer into the case!
If you built a drawer so the bottom edge will cover the support, check that the drawer edge covers the support before you glue the support into place.
Set the case aside to dry. If you wish, you can glue in a bottom toe kick and the overlapping case top at the same time as you glue in the drawer support.
If you aren't building a night table with drawers, but only with shelves, line the shelf up with the marks you made earlier and glue them into the case so the sides of the shelf are square with the case.
Set aside to dry
