You can store breast milk in a sterilised container or in special breast milk storage bags:

in the fridge for up to 8 days at 4C or lower (you can buy fridge thermometers online) – if you are not sure of the temperature of your fridge, or it is higher than 4C, use it within 3 days but if it is room teperature you can keep it upto 7 - 8 hours
for 2 weeks in the ice compartment of a fridge
for up to 6 months in a freezer, if it is - 18C or lower
Breast milk that's been cooled in the fridge can be carried in a cool bag with ice packs for up to 24 hours.

Storing breast milk in small quantities will help to avoid waste. If you're freezing it, make sure you label and date it first.