This is one where if you have the time and effort to dedicate to it, can be simple. You memorize your deck, so when they tell you the card, you thumb to it and flip it so when you fan it, the card they picked is upside down.
The "Invisible Deck" is a very famous trick. It can be purchased[1] for about $10 and just about anyone can master it in about 10 minutes. With the standard method, you don't need to memorize the deck or flip the card.
[1] https://www.amazon.com/U-S-PLAYING-CARD-COMPANY-SG_B002MI1B3...