The combat sequence in 1E AD&D is a simple procedure with a lot of special case exceptions that, taken in isolation, work fine but when combined quickly become a very big mess. The trick, then, is not to use the various special cases in combination -- when you've got, for instance, a high level fighter with multiple attack routines attempting to melee an enemy spell-caster who won initiative for the round don't try to apply both the rules for multiple attack routines and the rules for meleeing enemy spell-casters who won initiative together, because the two systems aren't consistent and were never intended to be combined. Instead, use common sense and make something up that seems appropriate -- that is the true "spirit" of the 1E AD&D combat/initiative rules, and all of the various complicated special cases laid out in those rules are nothing more than examples of how to handle various common situations, not ironclad rules, and certainly not a "system" in the modern sense.
Here's a few rules of thumb:
*Each round, both sides roll 1d6. Higher roll goes first, tied rolls equal simultaneous action. This is the general rule; everything else is exceptions.
*Characters cannot move more than 10' and engage in melee in the same round unless they're Charging (Note: this works both ways -- a character spending the round closing to melee range can't attack, but can't be attacked either, unless the opponent is Charging him).
*Charging characters may move up to their full Charge movement and melee in the same round -- first strike at the end of a charge is determined by weapon length, not initiative roll. Charging characters get an attack bonus but suffer an AC penalty. Characters can only Charge once every 10 rounds.
*Characters with missile weapons with ROF2 may move 1/2 and fire once, not move and fire twice, or move full and not fire. ROF1 (or less) may not move and fire in the same round. Exceptions: elves (and mounted archers) may move full and fire once, characters with thrown weapons (spears, axes, hammers, daggers, etc.) may move full and fire once (and, if Charging, melee at the end of the Charge).
*Characters firing missiles who are in the unencumbered (12") encumbrance class may add their Dex reaction bonus to their side's initiative die (so, if the party rolls a 3, the Dex 17 (+2 reaction bonus) archer effectively has a 5, which may cause him to tie or even beat the other side's roll).
*Spellcasters must declare which spell they are casting before initiative is rolled, may not move and cast in the same round, and may not apply their Dex AC bonus while casting.
*Characters who lost initiative to enemy spell-casters may still be able to interrupt the spells, by comparing initiative roll and/or weapon speed to the spell's casting time (there are two different systems for this in the DMG, and they're not consistent with each other).
*In melee, higher number of attack routines wrap around lower numbers, taking precedence over the initiative roll (so a character with 2 attack routines/round against a character with 1 attack routine will always attack 1st and last, regardless of initiative rolls).
*In melee, tied initiative rolls are broken by weapon speed; mismatched weapons might give the faster weapon extra attacks.
*Unarmed combat (DMG procedure) and Psionic Combat use different initiative procedures from normal combat. Unarmed combat (UA procedure) uses the normal initiative rules, but characters making unarmed attacks suffer an individual initiative penalty (which may cause them to tie or lose initiative even if their side won).
*Characters who aren't engaged in combat can perform a minute's worth of activity -- move up to their full move rate, cast up to a 10-segment spell (but only one spell per round, unless they;re both cantrips (from UA)), or other miscellaneous activity.
I think that covers just about everything in the rules. For anything that's not covered above, or where two or more special cases apply at once, you're on your own.
