For a long time I stopped playing AD&D (2nd edition), and my books were left to sit on a shelf. Recently, I have started to play again with friends and family, and we are going start a new campaign with new characters.
I wanted to use more than just the basic races and wanted to use an illithid (more specifically an alhoon) but I can't remember which rule book gives the information to play monsters and the like.
All I need is the name of the rule book, but if you are willing to share the exact ruling of how to use this race of character, I wouldn't mind.
You're thinking of The Complete Book of Humanoids. However, it doesn't present rules for how to play any monster, it provides only specific humanoid races with the specific statistics necessary to make a player-character of that race. Because of how AD&D 2e's player-characters work very differently from how monsters work, there's no way to systematically “translate” a monster's monster-stats into player-character–stats, and each new race option has to be designed (and playtested) by hand.
Notably, there are no options for mind flayers, and undead are specifically called out in TCBoH as inappropriate for PC race options, making an alhoon doubly unavailable.
That said, if you're the DM and want to provide that kind of option, there's nothing stopping you from looking at the race options presented and attempting to homebrew your own Alhoon option for your players. You're just mostly on your own, then.
The Complete Book of Humanoids has information on some monster races and Requiem: The Grim Harvest which is a Ravenloft book has information on how to make certain types of undead player characters. While they don't have stats for most monsters to use as player characters it should be simple enough to use the aforementioned books, the Complete Psionics Handbook, player's handbook and the monstrous compendiums to adapt the existing information for player character use.
Beyond the suggestions above I should recommend take in consideration the rules for monsters as players of 3rd edition's Monsters Manual/Dungeon Master Guide and mix it with the 2e DMG guidelines and CHHB rules to adapt powerful races like illithids/alhoons specifically. One more book can be useful for this: Ad&d Monstrous Arcana - the Illithiad.
So, In 3e DMG (page 23) we have a rule about monstrous races HDs that can fit better with a 'illithid/lich' who beggining at lvl 1 makes no sense:
If a monster has 2 or more Hit Dice, it can start with no class levels
(though it can gain them later)
The alhoon should have 9 'monster levels', it could begin casting spells as 9th level and with 8+4 HD, like its statistics from the 'Illithiad' (page 87):
Alhoons normally cast spells as 9th-level mages (Spells: 4/3/3/2/1).
However, they cannot cast spells in the same round in which they
psionically or physically attack. Alhoon: AC 5; MV 12; HD 8+4;
THACO 11; #AT 4; Dmg 1d4; SA psionic powers, spells: SD infravision,
immunities, unturnable; SW sunlight, subject to spells that affect
undead—excepting those detailed under Special Defenses below; MR 90%
Then it should begin to gain levels as mage, receiving d4 HDs, improving THAC0 at wizard rate, etc.
It is a very powerful option. If you consider that the worst disadvantage in Humanoids Handbook is for firbolg (page 29):
Firbolgs must earn double the experience points of the base class to
advance each level (for a fighter, 2nd level at 4,000,3rd at 8,000,
and so on). Firbolg Shamans: Firbolg shamans must earn triple the
experience points of the base clerical class to advance as shamans.
The GM could rule that a alhoon must earn triple or even quadruple xp.
Another rule from CHH that fits is monstrous traits, it could have:
Monstrous Appearance 3: Humanoid appears strange and frightening; -6
penalty to reaction checks.
As a powerful race, It could have a high maximum level as mage, since quadruple or triple xp limitations are the bottle neck here. So, the maximum level in CHH (with the exception of saurials) is 14 (swanmay), it could yet get pre requisite score above 3 points the maximum racial and reach level 17 (table 2 on CHH page 9).
And a +2 Int/-2 Cha modifier is plausible in a 2e campaign.
It is implicit here that the campaign should begin at level 9 to the group of adventurers.