Paint is kept best in air tight containers. If you're halfway through painting and need to store tins that are half full or more, remove the lid and cover the top with cling film. Replace the lid and label the paint product name and manufacturer, colour name or code, and date last used.
Have leftover paint? Tins less than half full should be decanted into something smaller with a tight lid, like a jam jar. Again, make sure you label the lid with the details as above.
Paint is best stored at a constant temperature, away from direct sunlight and in a frost-free environment. A garage or shed is great, or store in a dark cupboard in the house if you're worried about the weather.