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 phylactery ... can be fashioned into virtually any item, provided that it has an interior space in which the lich can carve certain small magical designs. Silver is poured into these designs, and a permanency spell is cast on the whole. The designs include arcane symbols of power and the wizard's personal sigil. ... The wizard's personal sigil is a mystical sign of personal significance, and identifying it may convey great power over a lich.
Once ... crafted and properly enchanted, four spells must be cast upon the phylactery: enchant an item, magic jar, permanency, and reincarnation. ... The manner in which the spells are cast and the time at which they are cast are not important, except that the permanency spell must be cast last of all. The rules ... are not immutable. ... The Dungeon Master is encouraged to customize not only the phylactery, but the process of creating it, too.
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:
... the mage may blend several forms of natural poisons, including arsenic, belladonna, nightshade, heart's worry, and the blood of any of a number of poisonous monsters. Also necessary are a heart, preferably from a sentient creature, and the venom from a number of rare creatures such as wyverns, giant scorpions, and exotic snakes.
... If any error is made in the formula or in the concoction and distillation of the potion, irrevocable death results.
When the ingredients are properly mixed, the following spells must be cast upon the potion: wraithform, cone of cold, feign death, animate dead, and permanency. The potion must be drunk during a night with a full moon. Upon ingestion, a System Shock roll is required. If the mage passes the test, then he has been transformed by the potion into a dreaded lich.
If the mage doesn't survive the shock, he is dead forever, with no hope of any sort of resurrection. Not even a wish will undo the lethal potion. Only the direct intervention of a deity (or the Dungeon Master) has any hope of resurrecting a mage killed in this manner.
It is worth noting that while rare, the book also describes priestly lich:
The cleric lich is created through the same process as is the wizard lich, except that the spells it casts are obviously clerical in nature.
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:
... A phylactery can come in any shape, from a ring to a crown, from a sword to an idol. The item is made from the finest materials and must be fashioned by master craftsmen. ... The cost of creating a phylactery is 5,000 gp per level of the psionicist. ...
... the psionicist must empower [the phylactery] with each and every psionic ability that he or she possesses. Although an object cannot normally be empowered with psychic abilities in more than one discipline, the unusual nature of the phylactery allows this rule to be broken. However, before "opening" a new discipline within the object, the would-be lich must transfer all powers from the first discipline into it. ... Once a discipline is "closed," it cannot ever be reopened.
... Each time that he or she gives the phylactery a new power, the psionicist loses it forever. ... Obviously, the last power that is transferred into the phylactery is the empower ability. The effort of placing this ability within the phylactery drains the last essences of the psionicist's life and completes the transformation into a psionic lich. At the moment that the transformation takes place, the psionicist must make System Shock survival roll. Failure indicates that ... the psionicist's spirit breaks up and dissipates, making him or her forever dead. Only the powers of a deity are strong enough to revive a psionicist who has died in this way; even a wish will not suffice.
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.