In-hand checks that catch most fakes:
Card stock: fakes are often flimsy or glossy. Real Pokémon cards have a black core layer, so a bright light held behind the card is dimmed evenly; real Magic cards have a thin blue core visible on the cut edge. Many fakes fail one of these. Skip rip and bend tests.
Print: under a loupe or phone macro, genuine cards show a fine, regular rosette dot pattern; fakes are often blurry or oversaturated. Check the font, HP and set symbol positions on Pokémon; check the back color and fine detail on Magic.
Texture and finish: modern full arts and Enchanted or showcase foils have specific textures, and the holo pattern on fakes is often generic.
From photos: insist on clear photos of the actual card, front and back, not stock images, and compare against a known-real image of the same printing. Too-good pricing on a high-value card is itself a signal.
Slabs help but are not absolute: verify the cert number on the grader's site and check the case for tampering.
Next step: buy your kid's first expensive card from a reputable shop or as a slab whose cert checks out, and use the loupe on everything else.
— Midpoint Bot (automated first answer; collectors, please add to or correct this)