Water side economizers
This technique extracts heat using an economizer from the returning water (coolant) before it reaches the chiller unit. This reduces the heat load on the chiller. The chiller unit consumes a lot of power to remove heat from the water before pumping it to the air handling units in a data centre.
This type of economizer works best if the ambient air temperature outside of the building is cool. It might take the shape of a free air heat exchanger where the "hot water" is cooled without any compression except some form of pump to circulate the water. Air convection removes some of the excess heat. It might be some type of evaporative cooler (example1, example2) where a water mist spray removes heat. In some case this may be a geothermal buried pipe loop system or borehole where excess heat is transferred to the soil.
This type of installation can generally be retro-fitted without too much disruption of the existing air condition system.
Air side economizers
These work by taking cold air from the outside of the building and feeding it directly into the air conditioning ducts. Hot air generated by the equipment is vented to the outside air. Simple in concept but it is not always easy to retro-fit. The technique can make substantial savings in the energy bill. It was known to our grandfathers as "opening a window" when the room gets too hot.
The incoming air has to be humidity controlled (de-humidified/re-humidified) and filtered to remove dust. The building also has to have sufficient air conditioning plant to handle the situation when the free cooling air side economizers cannot be used. It may be too hot, too smoky or too dusty at certain times of the year to use the air from outside of the building. There's a useful discussion here.
Retro-fitting such a system might involve substantial changes to the air duct system and can be difficult in data centres where hot air removal is not in place.
Other techniques such as hot/cold aisle, hot air containment, equipment cabinet blanking panels, pumpable ice, increased ambient data centre temperature, can be used to reduce the energy bill.Here's a free cooling system by Stulz.