The D&D lich was introduced in the Greyhawk supplement as type of undead created when a spellcaster uses powerful magic to defy natural death:
[S]keletal monsters…of magical origin, each Lich formerly being a
very powerful Magic-User or Magic-User/Cleric in life, and now alive only by means of great spells and will because of being in some way disturbed. – Dungeons & Dragons Supplement I: Greyhawk, TSR 2003
In Advanced Dungeons & Dragons 2nd Edition, were there rules given for how a player could become a lich?
Best Answer
While there are various sources, such as the Monstrous Compendium and the Wizard's Spell Compendium, as described in the answer by Mark Beadles, arguably the most inclusive source is the Van Richten's Guide to the Lich, a sourcebook of about 100 pages dedicated entirely to the lich. It describes two ways for becoming a lich, one magical (for wizards and clerics), the other through psionics.
To become a lich through magical means, one first needs to prepare a very expensive (1,500 gp per level of the wizard) phylactery of exquisite craftsmanship. The phylactery is usually a box, but it can also be some other item with some interior space:
The next step is the preparation of a highly poisonous potion of transformation, which needs to be consumed on a night with a full moon:
It is worth noting that while rare, the book also describes priestly lich:
To become a psionic lich, the psionicist must be of at least 18th level and must be trained in variety of psionic powers. Again a phylactery is prepared and the would-be lich transfers his/her powers into it:
PS: As mentioned in a comment by @TimothyAWiseman, Van Richten's Guides are Ravenloft source material. But the books are written in a way that seem to imply that they broadly apply to all AD&D 2e settings, with "in-game" and sidenote examples from Oerth, Toril, etc. For example VRGttL lists Azuth, Beshaba, Cyric and Mystra as possible dieties for the cleric lich.
Alternatives: Archlich & Baelnorn
If the lich candidate is good or neutrally-aligned and does not want to become an evil undead, the alternative is to become an archlich, whose procedure is described in the answer by ucbpaladin. Yet another alternative in the Forgotten Realms setting is the baelnorn lich. These are usually LG or LN elf undead with lich-like features. According to Cormanthyr: Empire of the Elves, the procedure for becoming a baelnorn is through the elven high magic ritual known as "Fhaor 'Akh 'Tel'Quess - Tribute of One's Duty to the People". For some details you can see the book itself, which used to be offered as a free download by the Wizards of the Coast.