memo, note (usually notepad), scratch (AmE)
drawing, sketch
writing
prescription

on a/the pad
She doodled on a pad as she spoke.

thick
adhesive
cotton (AmE), cotton-wool (BrE), foam, gauze, gel, rubber
polishing, scouring, steel-wool
menstrual (esp. AmE), sanitary
incontinence (esp. BrE)
mattress, sleeping (both AmE)
mouse (esp. AmE) (usually mouse mat in BrE)
Every computer user should have a good mouse pad.

heavily
She was wearing a warm coat and heavily padded gloves.

well

with
The shoulder straps are padded with foam.

quietly, silently, softly
barefoot
about (esp. BrE), around
He padded around in his socks eating cereal.

about (esp. BrE), around
She padded softly around the house.

across
He padded barefoot across the carpet.

along
The cat padded silently along the track.

to, towards/toward

Pad is used with these nouns as the subject:
cat

Pad is used with these nouns as the object:
résumé