Since I don't trust myself to lay the fabric perfectly straight inside the drawer, I cut the fabric slightly larger than needed. I did this by tracing the drawer and cutting a 1" border on all sides.
(I don't have a photo of this process, but you got this!)
STEP 2: Spray Adhesive
Prep: Tape along the side walls of the drawer and wrap the sides with scrap paper / newspaper so the sides of the drawer don't get sticky from the spray adhesive.
Read the manufacturer's instructions on the can of spray adhesive (typically involves lots of shaking).
With broad strokes, coat the entire bottom of the drawer with spray adhesive, holding the can 6-8" away from the surface.
Tip: I highly encourage doing this process outdoors, as spray adhesive is not only toxic but will also make everything it its radius sticky. So, so sticky.
STEP 3: Add Fabric
Press the fabric down inside the drawer, smoothing out any wrinkles. Using a ruler (or similar straight edge object), press down the fabric into the edges and corners of the drawer bottom to make sure the fabric is thoroughly adhered to the bottom and pressed into the corners.
Tip: Some loose fiber fabric types (such as felt) may not peel back up easily if you get a big wrinkle. To make the felt easier to handle, I folded in the edges and rolled my fabric around a spare paper towel roll that I cut to fit inside the drawer. Starting at one edge, I slowly rolled it out out inside of the drawer and then used a ruler to press down the corners and edges.
STEP 4: Trim Edges
Remove the tape and paper used to protect the sides from the spray adhesive. Using a sharp X-Acto knife, trim the leftover edges of the felt fabric. If your fabric starts to fray, you might want to check the sharpness of your blade.
Tip: Turn the drawer on its side and run the blade against the sides of the drawers, angling the blade into the corner of the drawer. This will help you cut in a straight line, giving you more control of the blade. Slow and steady will lend a better result. Going too fast and the blade might get away from you!
STEP 5: Glue Edges
To ensure the edge of the fabric wouldn't peel up over time, I put a bead of Elmer's Glue around the edges of the felt, spreading it with my finger so it would dry clear. You can also use Tacky glue if you prefer.