Surface layer of dust and dirt should be removed by vacuuming or brushing tiles. Furniture should be covered to protect from the dust that settles.
Enzymatic cleaning agent, specially designed for acoustic tiles, should be used to remove grime and embedded dirt.
Stains that can't be cleaned should be covered with special product that will not affect acoustical of fire ratings.
On a side note, make sure HVAC ducts are cleaned and filters regularly replaced to minimize dust that could otherwise stick to your acoustic tiles.