empty
full
half-empty, half-full
broken, chipped, cracked
china, porcelain
disposable, Dixie™ (= paper cup), drinking (AmE), paper, plastic, polystyrene (BrE), Styrofoam™ (AmE)
tin
coffee, tea
egg
yogurt (AmE)
measuring (AmE)
sippy (= for babies)

fill, refill
drain, empty
She was so thirsty that she drained her cup.

lift, pick up, raise
She raised her cup to her lips.

place, put down, replace, set down
drink from, drink out of
Customers don't like drinking out of plastic cups.

contain sth

holder

a cup and saucer

strong
I like a good strong cup of tea first thing in the morning.

fresh
My coffee was cold, so I ordered a fresh cup.

hot, steaming, warm

offer sb
make (sb)
pour (sb)
I'm making tea. Can I pour you a cup?

buy, order
help yourself to
stir
Enrique stirred his fourth cup of coffee of the day.

drink, enjoy, have
I drink about ten cups of coffee a day.

sip
finish

cup of

a nice cup of tea (BrE)
You sit down and I'll make you a nice cup of tea.

challenge
knockout
American, European, World, etc.
gold, silver

win
Who won the cup?

lose
present (sb with)
The cup will be presented to the winning team by the president.

lift, raise
He lifted the cup for the sixth time this year (= it was the sixth time he had won).

competition
They were the first Turkish team to win a major cup competition.
the Ryder Cup competition

clash (BrE), match (esp. BrE)
The team are ready for next week's World Cup clash with Italy.

race
final, quarter-final, semi-final (all BrE)
victory, win
winner
holder
contender, hopeful

the first, etc. round of the cup