In my experience ( Arnold Arboretum and Filoli Estate ) the process was basically the same .
Run a de-thatching machine across the lawn. North to South and then East to West.
rake up and compost the thatch.
Run an aerator machine , the kind that pull plugs out, across the lawn.
Broadcast a mixture of sand and fertilizers/ composts across the swiss cheese looking lawn .
In some cases over seed - other cases over seeding not required due to type of existing variety of lawn.
water.
mow.
water
mow
lather , rinse, repeat.