The basics: sleeve and toploader
A loose card degrades from simple friction against other cards. The bare minimum is a thin plastic sleeve (penny sleeve) on the inside and a rigid toploader on the outside, which keeps it from bending or getting scratched.
For more valuable pieces, semi-rigid cases ('magnetic case' or 'card saver') exist that also protect the corners better — the spot where wear shows up first.
Where and how to store them
Avoid direct sunlight: it fades ink over time, especially on cards with intense color areas.
Avoid sudden swings in humidity and temperature: they can warp the cardboard or stick the card to its sleeve. A closed cabinet or box at a stable temperature is safer than a spot near a window or a radiator.
Always store them upright in a box designed for cards, not stacked flat with weight on top: constant weight can also warp them.
Mistakes that lower a card's value
Touching the surface with bare fingers: skin oil leaves marks that sometimes never come off, and directly affects the grade if it's ever submitted for grading.
Leaving it unsleeved "just for a few days": a single bump or drop is enough to permanently mark a corner.
Shipping it poorly protected: a plain envelope with no rigid backing is the most common reason a card arrives bent. Any shipment should include, at minimum, a sleeve + toploader inside a rigid mailer or box.