First level Clerics and Druids can pick any spells from their respective lists. Probably done to balance the fact that their selection have few offensive spells and each class involves following a religion.
On DMG p.39 there is a chart that you can use to determine the initial spells of a starting Magic User. The page explains the procedure; the end result being the magic-user has Read Magic plus 3 or 4 additional spells.
Illusionists have a different procedure that results in 3 initial spells.
Minimum Known Spells and Chance to Learn Spells work as follows.
Magic users and illusionist write down spell in a spell book. The spell book is required to be present in order to memorize a spell. A magic user has a limited number of slots in use to memorize spells. Once cast a spell (or another spell) can't memorized in its place until the magic-user has rested for a period of time. This is given on page 40 and applies to all spell using classes. The spell book is required to be present to study from in order to memorize spells.
Intelligence affects the ability of the magic-user/illusionist to scribe spells into his or her spell book. A spell can be either independently researched or copied from a scroll or spell book. When this occurs you roll your chance to learn spell. If you succeed you copy the spell into your spell book. If you fail you don't and can't memorize that spell as it beyond the character's understanding.
You keep track of both the spells that the magic-user failed to learn and succeeded in learning. If you run through all the spells at a particular level and you did not manage to copy the minimum number of spells then you reset the failures and the character gets to try until he fills his spell book with the minimum number for that spell level. There is a maximum number of spells as well per spell level also based on intelligence.
Spells may require material components to cast. This is found in the Player's Handbook in the description of various spells. There are codes of V,S, and M which stand for Verbal, Somatic (hand gestures), and Material Components. The spell text will list the required components.
In practice, most AD&D referees will only require material components when they are of significant value or rarity. Like the Magic User 9th level spells Shape Change which requires a jeweled circlet worth 5,000 gp. Most AD&D referees in my experience look at the Verbal and Somatic requirement to handle specific situation like when the spell caster is tied up or gagged.
This of is all explained with additional details on pages 38 to 40 of the Dungeon Masters Guide and in various sections of the Players Handbook.