I have thought about this question literally for years, and what I have come up with is based on what the best magic teachers in the world have taught me. Who are those teachers? The LAYMEN for whom I have performed. What have I learned. Well, first when having someone select a card, it is super-important that they believe they had a free choice. Second, it is equally important that they are absolutely convince that we are not controlling their card and that it is truly lost in the deck. I have seen renowned "card men" have someone pick a card, then swing cut and tell the spectator to place their card on top of the cut portion, or offer the cut portion to them implying that they are to place their card on top of it. This is not good!!! Why? Because they do not want to replace their card where the magician tells them to; they want to put it back where THEY want to, to assure themselves that the sneaky magician, who they (justifiably) do not trust cannot deceive them and control their card.
In other words, if they do not (1) feel certain they had a free choice of cards, and (2) that the card was not controlled but rather hopelessly lost in the deck, it won't matter how "phenomenal" the ultimate revelation is. The card could end up in the hand of the Statue of Liberty and it won't matter, because the underlying conviction of fairness was not first established. The other thing I should mention is that spectators don't like to be told to "pick a card." Most often they have seen poorly done card tricks by their Uncle Harold or grandfather or some friend or acquaintance that began with that cliche of "pick a card." Sometimes, if you start a trick that way, they will even say, "I've seen that one before." Not good...
So, what do I do to satisfy the criteria I outlined? Well, I will start by giving one of several methods I use that works very well, and is never questioned. First, have them shuffle the deck themselves. This satisfies them that the cards are in a random order, that you could not know, with no set-up, and establishes fairness from the get-go. Then, tell them that you would like them to "select a card at random." Begin to slowly Hindu shuffle the deck, peeling off very small packets, and tell them, "Please say stop anytime you feel like it." When they say "stop," push over, with your left thumb, the top card of the packet of cards remaining in your left hand (assuming you are right-handed). Hold the card up for them to look at, while you turn your head away, and ask them to, "Please memorize that card." Ask them if they've got it? When they say yes, pull the card pack flush onto the packet in your left hand with your left thumb (again, this is assuming you are right-handed). Bring the cards you have in your right hand directly over the left hand packet, and, holding a break over the packet below (i.e. over the packet in your left hand on top of which is their selection). Start Hindu shuffling again and continue shuffling off small packets with the Hindu shuffle until you reach the break and then throw the remaining packet of cards in your right hand on top of all. The selection has been controlled to the top.
Hope this helps!