Trim the ends from the red onion and cut it in half from root to tip. Peel away the outer skin, then place the onion halves cut-side down on a cutting board. Thinly slice the onion into half-moon slices. A mandolin works well for very thin, even slices, but a sharp knife works just fine.
Place the sliced onion in a pint-size mason jar or similar heatproof container, gently packing the onions down so they reach near the top of the jar (if you have extra onions, use them for another purpose).
In a small saucepan, combine the apple cider vinegar, water, sugar, and salt. Bring to a gentle simmer, stirring until the sugar and salt dissolve.
Pour the hot pickling liquid over the onions. At first, the brine may not completely cover the onions, but they will soften and settle quickly. After a few minutes, press the onions down with a fork so they are mostly submerged in the brine.
Let the onions stand at room temperature for about 30 minutes before using. The onions will soften and turn bright pink as they sit. After they have cooled slightly, transfer the jar to the refrigerator.
Store in an airtight container in the refrigerator for up to 2 weeks. Make sure the onions stay fully submerged in the pickling liquid for best flavor and storage.