DIAGNOSIS Standard glass cleaners or household sprays often leave residues or can damage the anti-glare coating. The smearing means you're just moving the oils around.
FIX Power it off first (swipe down for settings and tap Power Off). Use a dry, soft, lint-free microfiber cloth—the kind for glasses or cameras. Gently wipe the screen in a circular motion. For stubborn fingerprints, slightly dampen a corner of the microfiber cloth with only distilled water. Wipe the screen with the damp corner, then immediately dry and polish with the dry part of the cloth. That's it.
IF THAT DIDN'T WORK For sticky residue (like from kids or cooking grease), use a cloth dampened with a 50/50 mix of distilled white vinegar and distilled water. Vinegar is a mild degreaser that evaporates cleanly. Again, apply sparingly to the cloth, not directly to the screen, and dry immediately. Test on a corner first if you're worried.
HEADS UP Never use abrasive cloths (paper towels, tissues), compressed air (can force moisture inside), or any cleaners containing ammonia, alcohol, or abrasives (like Windex, Clorox wipes, or hand sanitizer). They will permanently degrade the screen's coating, making it look hazy and increasing glare.