No two people can 100% agree on how AD&D initiative worked, but here are my 2 coppers:
After surprise is resolved (that is a WHOLE other post) spell casters must declare their spells.
Both sides rolled a d6, generally high wins initiative and goes first, with the understanding that movement is outside of the initiative process (if you want to move, you can start at segment 1, even if you lost initiative).
EXCEPT>>>>
If a missile weapon user is firing at a spell caster, and lost initiative, the spell caster must still compare their casting time against their own initiative roll. If the casting time is greater than the initiative roll, the missile hits first. If the casting time is less than the initiative roll, then spell goes first. Tied initiative goes to the missile attacker.
If a spell caster is casting against another caster, compare casting times, with lower going first. If casting times are equal, default to initiative order. If CT's are equal, and initiative order is tied, spells are simultaneous.
If a melee attacker is charging a spell caster (melee range is considered within 10 feet in the dungeon and 10 yards outdoors), you must compare the movement time in segments to the casting time. If movement is closed to within 10' before the casting time, melee goes first. If movement is closed to 10' on the casting time segment (3 segments of movement against a 3 segment spell) then default to initiative order. If initiative is tied, it is simultaneous.
If a spell caster is trying to cast WITHIN melee, and the melee attacker lost initiative, determine the absolute value of the Weapon Speed Factor minus the losing initiative roll. If the absolute value is higher than the casting time, the spell goes first. If the ABS value is less than the CT, the melee attack goes first. If initiative is tied, just compare the WSF to the CT, lower goes first.
When it is melee vs. melee, standard initiative is the default. UNLESS one player has multiple attacks, in which case that attacker always goes first AND last, regardless of initiative. If BOTH have multiple attacks, the initiative winner goes first and third, and the loser goes second and fourth. If there is a third extra attack, it goes last.
Melee v. melee when there is no multi-attacks, and the initiative is tied, defaults to Weapon Speed Factors, lower goes first. If the difference between WSF's are large enough, the faster weapon can get multiple attacks.
During a charge, initiative is not used - the longer weapon goes first.