heavy, thick
floral
silk, velvet, etc.
hanging

close, draw, pull
The heavy drapes were drawn shut.

open, pull back

hang
cover

casually, loosely
elegantly

across, over
around, round (esp. BrE)
He sat with his arm draped casually around her shoulders.

be draped in sth, be draped with sth
The body was draped in a blanket.

Drape is used with these nouns as the object:
banner, casket, cloak, jacket, shawl, towel