full-time, part-time
permanent, temporary (esp. BrE)
skeleton
We'll be down to a skeleton staff over Christmas.

experienced, professional, qualified, skilled, trained
junior, senior
ancillary, support
general (= officers assisting a military leader in administration and planning)
ground
the ground staff at the airport
The Wimbledon ground staff pulled the covers over the courts. (BrE)

academic, administrative, campaign (esp. AmE), editorial, news (esp. AmE), etc.
the campaign staff of President Bush

nursing, teaching (BrE), etc.
hospital, hotel, library, office, etc.
bar, catering (esp. BrE), door, kitchen, wait (AmE), waiting (BrE), etc.

employ, have
The company has a staff of fifty.

appoint, engage (esp. BrE), hire, recruit, take on (esp. BrE)
staff appointed to the project
I've heard they're recruiting staff at the moment.

dismiss, fire, lay off, make redundant (BrE), sack (BrE)
The bank expects to make 15 000 staff redundant over the next three years.

retain
Some companies are struggling to retain skilled staff.

train
pay
They pay their staff weekly.

join
He joined the editorial staff in 1999.

leave

work
The staff are working under pressure. (BrE)
The staff is working under pressure. (AmE)

deal with sb/sth, serve sb/sth, treat sb/sth
You want your best staff dealing with the best customers.
The bar staff can serve around a hundred drinks an hour.
the medical staff who treated him during his confinement

carry sth out
Specialist training is necessary for staff carrying out this work.

member (esp. AmE), person (AmE)
There are four full-time staff members.
a staff person for a government agency

position (esp. AmE)
a staff position at ‘Life’ magazine

levels, numbers (esp. BrE), resources
shortage
retention, turnover
cuts
appointment
The hospital is freezing staff appointments as part of its cutbacks.

development, training
wages (BrE)
accommodation (BrE)
There is separate staff accommodation for the housekeeper.

morale (esp. BrE)
meeting
association
canteen (esp. BrE), restaurant (esp. BrE), room (usually staffroom)
attorney, physician, scientist, etc. (all AmE)
She's a staff scientist at the Research Institute.

photographer, reporter, writer, etc. (all esp. AmE)
He's a staff writer for The New Yorker.

report (AmE)
a staff report by the House Foreign Affairs Committee

on the staff (of) (esp. BrE)
She has been on the staff of the hospital for most of her working life.

chief of staff (= in the army, navy, etc.)
member of staff (esp. BrE)
There are four full-time members of staff.

well
fully, properly
The ward is now fully staffed.

adequately, inadequately

be staffed by sb, be staffed with sb
The office will be staffed mainly with volunteers.
The reception desk is staffed entirely by experienced employees.

Staff is used with these nouns as the subject:
volunteer, worker

Staff is used with these nouns as the object:
clinic