Sometimes you mix a great color using your palette but then you have to put your work aside for the evening or even longer. So, how can you preserve the colors on your palette until you're ready to use them again?
Light, Air, AND Temperature. After restricting the air flow like by putting the palette into a container you can put it in the fridge or even the freezer for a longer period.
Some painters immerse the working palette into a recipient of water in the fridge for the best air restriction, because it is oil based the paint is not altered and is workable within an hour of removing from water.
It's fine to store your oils in the freezer if you're taking a break. The cold temperature will slow the rate of oxidation and evaporation, preserving the paint.(...) "...by early Renaissance times professional supplies of pigments existed ... Prepared oil paints were kept in the studio under water to prevent them from drying out."
Using left over paint within " the evening or even longer" should not require any special method. Otherwise, if you add oil to the paint before setting the palette aside it will be work able for days longer, and even longer with a slow dry medium.
The best way is still to use paint little by little so not to have too much left over.
If you're working with oil paint? Nothing is needed! Paints on a palette will remain workable without any further interaction for a couple of days. Longer than this, consider putting some cling film carefully over the top. If the paints have gone a bit stiff when you come back to them, simply work them carefully with a bit of white spirit or turpentine to loosen them again.
For longer storage, you can seal the paint inside of an empty paint tube if the amount is fairly large. These can be purchased at better art stores for a couple of dollars and basically lets you work with it like it was any other paint in a tube.
For smaller amounts, you can go your own with aluminum foil. Basically, create a small pouch, doubling up to give it strength, fill it with your paint, then seal it off from the air.
My mother has been painting professionally for over 70 years, using oil paints. She keeps a fridge in her studio and puts the palette in the fridge overnight at the end of each session, when she has colours mixed that are not used up. Being in the fridge keeps them in the dark as well as keeping them cool (she has spent most of her career in warm countries). If she knows that it may be a few days before she can paint again, she uses clingfilm or similar as well - for longer storage, she puts the palette under a cover as well as using film.
Clove oil slows the curing, or cross linking, of linseed based oil paint. I use a small sponge in a bottle cap and put a few drops of clove oil on it. Then I place the clove cap on my palette (which is a glass sheet inside a covered rectangular Tupperware) and cover it. Oil paint will stay fresh for a week or more.