AD&D PHB p 20:
When a cleric achieves 8th level (Patriarch or Matriarch) he or she automatically attracts followers if the cleric establishes a place of worship -a building of not less than 2,000 square feet in floor area with an altar, shrine, chapel, etc. These followers are fanatically loyal and serve without pay so long as the cleric does not change deities and/or alignment.
AD&D PHB p 32:
When a monk player character attains the 8th level of experience, he or she will gain a number of monks as followers upon defeating the monk which held the 8th level position that the player character has now gotten. . . . Note that monk followers require no support, upkeep, or pay of any sort.
I assume that a ranger's followers, a fighter's mercenaries, and a thief or assassin's gang/guild members, have loyalty calculated in the normal fashion, but the rules don't really specify. (The text for fighter's was already quoted upthread, I think (PHB p 22): "These men will serve as mercenaries so long as the fighter maintains his or her freehold and pays the men-at-arms".)
As to why these various NPCs turn up to serve the PC, the DMG addresses that:
AD&D DMG p 16:
Your players know that upon reaching certain levels and doing certain things (such as building a stronghold) they will be entitled to attract a body of followers. These followers might be fanatically loyal servants of the same deity (or deities) in the case of clerics, stalwart admirers of fighters, or whatever.
I know that it is common for posters to assert that the D&D GM is not subject to any rules, and that the GM can make up whatever fiction they like that they think makes sense as coming downstream of some PC action; but the text just quoted is yet another counter-example to that contention: once the PC reaches the requisite level and the player has them do the relevant thing, then the GM is obliged to create fiction which includes the appropriate followers turning up to serve the PC in the appropriate fashion.