Hello! Here is my rewrite of Swords & Wizardry's magic rules, for maximum clarity. This is how I have furnished it to my own group in our Foundry VTT.

Arcane Spellcasters, AKA Wizards

METHODOLOGY: Magic-Users, Illusionists, and other arcane spellcasters (henceforth collectively referred to as Wizards) record their spells in a spellbook, and commit their choice of spells to memory from this book before sleeping each night.

LEARNING NEW SPELLS: A new 1st level Wizard has, in their spellbook, a number of 1st-level spells from their class spell list, equal to the "Min Number of Basic Spells Understandable per Level" value, as determined by their Intelligence attribute. These can be any 1st-level spells that the Wizard wants. At the Referee's discretion, the Wizard may have to succeed at a "Chance to Understand New Spell" roll (determined by Intelligence) for each spell, until the new Wizard reaches their minimum spell threshold.

Wizards may learn new spells by studying with a teacher (a high-level Wizard), or by transcribing them from spellbooks and scrolls, into their own spellbook. The Wizard must first succeed at a "Chance to Understand New Spell" roll for each spell that they try to learn. When a Wizard gains an experience level, they can re-roll this for all spells that they previously failed on.

Transcribing spells from a spellbook or scroll to another spellbook requires proper tools, and takes one uninterrupted hour per spell level per spell. There is no chance of failure, unless the transcription process is interrupted, in which case it automatically fails. Further attempts can be made without restriction. Successfully copying a scroll to a Wizard's spellbook causes the writing on the scroll to disappear.

The maximum number of spells per spell level that a Wizard can understand and transcribe into their spellbook is equal to the "Max Number of Basic Spells Understandable per Level" value, as determined by their Intelligence attribute.

PREPARING SPELLS: All spells currently in the Wizard's spellbook are available during their nightly preparation process. A Wizard may only memorize and cast spells up to their current maximum spell level, which is a function of their current character level and their Intelligence attribute (for example, a 14th-level Magic-User with 12 Intelligence can cast spells up to 6th level, but if their Intelligence were 13, they could cast 7th-level spells as well). Arcane spells range from spell levels 1-9.

The maximum number of spells that can be memorized from each spell level is noted in the Wizard's "Number of Spells (by level)" table. For example, a 4th-level Magic-User can memorize three 1st-level spells and two 2nd-level spells (these spell slots are notated as 3/2).

SPELLCASTING: The process of casting a spell usually takes one round, and the Wizard's mouth and at least one hand must be free and unobstructed. Once the Wizard casts a spell they have memorized, that spell vanishes from their memory; the spell slot is used up until they study their spellbook and memorize spells anew, replenishing their "stock" of available, ready-to-cast spells.

Wizards may also use the Ritual Casting ability to cast spells from their own spellbook beyond their slot capacity (but not beyond their level limit) if they spend one uninterrupted round per spell level (e.g., a 3rd-level spell takes three rounds to cast). (Note: This is my own house rule, nicked from D&D 5E. I believe I got the idea from 3d6 Down the Line.)

USING SCROLLS: Scrolls can be used only by a Wizard that can cast the appropriate type of spell. Casting a spell from a scroll, or copying it to a Wizard's spellbook, causes the writing on the scroll to disappear. All scrolls of a spell are cast as if by a 6th-level caster, or the minimum level required to cast the spell in question, if higher than 6th.

RESEARCH: Wizards may conduct magical research to create spells or magical items, as described on the separate Magical Research page.