You need a cardboard template, velvet and glue.
Make a cardboard template — its parts should tightly fit your drawer.
Recommendation: better leave 2mm of height free of velvet.

Apply and cut off the excess:

Cut off the template + 1-1.5 cm for allowances.

Apply PVA glue on the cardboard:

Fold and glue the edges. Cut off excess fabric:

Leave it to dry for 15-20 minutes, put under a press.

Apply glue with a brush to the back side of the cardboard and gently attach it to the box. Piles at the edge can be neatly cut off with scissors.

Leave to dry under a press.

All is ready! :)

All is done!

In addition, I offer you a video tutorial:

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Wish you much success!