At home - HOT soapy water in a bucket with a length of plastic tube that fits over the nipple. Other end of the tube goes in the bucket. Poor some hot water into the barrel to prime the pump, put a tight patch on the cleaning rod and start pumping. Then I rinse with HOT water (because it evaporates quickly) a dry patch and then a lightly oiled patch.
In the field - Hoppes #9, dry patch and then oil.