Empty the drawer and remove it from dresser.
Dust or clean the surface of the drawer to be sure the velvet adheres properly.
Measure all the sides that you want to line with velvet.
Cut out strips of velvet adhesive that correspond to the measurements that you took.
Peel back the top edge of one the rectangles, separating the velvet from the non-adhesive backing by 1 inch.
Press the adhesive side of the velvet to the corresponding side in the drawer, lining it up neatly to the corner.
Peel the non-adhesive backing away, pressing the adhesive edge to the drawer surface, until the velvet covers the drawer.
Repeat Steps 4 through 6 until drawer is completely lined.