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Above all, avoid leaving them near heat sources or in environments with temperature fluctuations. One trick not many people know is to wrap the models in newspaper before putting them in a box: the ink absorbs moisture better than you'd expect, and it costs basically nothing.
Yellowing of model kits is mainly caused by UV light exposure and humidity - two enemies you can easily control. The simplest solution is to store them in a closed box in a dark place, ideally on a shelf inside a cabinet or away from windows. If you want to keep them visible, a display case with opaque doors is ideal because it protects them from direct light while keeping them in sight.
Humidity is the second serious problem. If you live in a particularly humid area, put small silica gel packets (the ones you find in shoe or medicine boxes) inside the box or display case. Change them out occasionally or put them in the sun when you take them out if they've gotten damp. Fresh air is your friend, so avoid dusty basements or rooms where condensation forms. If you really want to store them perfectly, a sealed box with silica gel inside a dry location works best.
One detail a lot of people overlook: don't keep them in direct contact with cheap plastic, because it reacts chemically over time and promotes yellowing. Paper or cotton bags are safer. And if you take them out now and then to look at them, always do it with clean, dry hands.
Don't keep them in direct sunlight or under overly bright LED lamps, because that's the number one killer. What really works is putting them in an opaque box in a cool, dry place, maybe with a silica gel packet if humidity is an issue in your home. If you really want to display them, at least use a display case with UV-blocking glass, so you can see them but keep them protected.
If you really want them to last without yellowing, the most effective thing is to use vacuum-sealed bags together with small silica gel packets. It's not complicated: put the model in the bag with the desiccant gel, remove the air and seal it all up. That way you control both humidity and oxidation, which is mainly what causes the yellowing over time.
Then store the bags in an opaque box in a cool place, ideally not in direct contact with the house's outer walls where it can get hotter or more humid. I learned this trick while organizing an old toy collection for a friend, and honestly it makes a huge difference. If you don't want to spend too much on silica gel, you can recycle those little packets you find in supplement or shoe boxes - just dry them out in the oven on low heat when they absorb too much moisture.
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