Now, the way I imagine this preparation is based on grimoires (like Francis Barrett's The Magus, freely available on the net) plus Giordano Bruno's approach to memory palaces: the magician does some astrological calculations to figure out which planets govern the kind of spells being prepped, performs some rituals binding magical forces to key mnemonic phrases and gestures, and then invokes each spell at the desired moment by gesturing and reciting the key phrase. I've talked about this in more detail before.
But that's not important, not only because the prep happens during downtime, but also because I want to focus on what the rules actually say about spell prep. Here's the relevant quote from the 3LBBs:
The number in each column opposite each applicable character indicates the number of spells of each level that can be used (remembered during any single adventure) by that character. Spells are listed and explained later. A spell used once may not be reused in the same day. (Men & Magic, p. 19.)That's it. There's another section about spell books, but that just talks about how much they cost; it actually doesn't say anywhere that spell books are used for spell prep. Nowhere in the rules does it specify how long spell prep takes, probably because the way time was tracked assumed one real day = one day of downtime in most cases, and expeditions were short: PCs would head to a dungeon, explore a bit, return to town, re-provision, and head back for another go. Spell prep was just assumed ro be part of the downtime, but because the usual time between excursions is at least a day, I think a one-day prep time is a reasonable assumption for a loose OD&D game.
I don't know what B/X or BECMI did, but AD&D set exact spell times based on spell level. This has more or less seeped into the community consciousness, so most people state a house rule about spell memorization taking 15 minutes, 30 minutes, or an hour per spell level. I had a similar scheme, but I simplified things by basing the total time for all spell prep on the highest spell level prepared, instead of counting individual spells.
However, an alternative might be to assume a flat four-hour period to memorize up to four spells of a given level, based on the spell progression on the magic-user experience table. This fits with the idea I expressed in those recent comments: magic-users who have just learned spells of a given spell level take a full four hours to prep one spell of that level, because they're less confident. A magic-user's confidence increases with every level increase, enabling them to pack more spell prep into the same amount of time.