You usually leave it on during the day as well, especially if it is at least somewhat opaque, since that will reduce chlorine loss during the day from sunlight. Having the cover on during the day will also reduce evaporation (and subsequent refill assuming you have an auto-fill) so will keep water parameters such as TA and CH from rising from the fill water. You generally take the cover off when you want to use the pool. You might find that the pool is too warm during the hottest part of the summer in which case you could take off the cover some nights to cool it. If the cover is mostly clear, then taking it off during the day will also work since it will reduce the temperature of the water via evaporation.
If you aren't using the pool regularly, you should still take the cover off at least once a week or so to have the pool air out and get some exposure to the UV in sunlight. This helps prevent formation or accumulation of some disinfection by-products.
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