There are some fluffy mechanics out there.
If you want spell formulas or potion recipes like the lich has, you are probably not gonna find them for the "lesser" undead. That said, the fluffy methods, while less defined, allow for several in story methods for a PC transitioning.
Best (most comprehensive) Source
The Requiem: The Grim Harvest boxed set for Ad&d 2e has a whole section on playing undead. The information starts on page 29 of the Requiem book. This includes a section titled From Life To Unlife. This section details the game mechanics to transition from a PC with levels to an undead PC.
With these rules one can play a:
An Article in Dragon Magazine #234 called Undead Again: More Undead PCs for the Requiem Campaign (pg 28) added 3 more to this list:
- Crawling Claw (dowhatnow? But I am not joshing, apparently they thought it was playable.)
- The Penanggalan (At least it has a head, Mr. Crawling Claw)
The next section details how you might advance in such classes as Skeleton or Zombie. It also covers dual classing in your new character class.
As far as in game methods to affect this transition, this supplement assumes it happens in a demiplane wide catastrophe, caused by an item cleverly titled the Doomsday Device. However, beginning on pg 70 there is an entire section on in game justifications about how and why a PC becomes undead.
Some (not all) justifications include:
- Sudden Death
- Dark Pacts
As a note, the book also contains a section for undead character classes, to be used at character creation, as opposed to being "died" into this state. There is even a section on how you might return to life.
Other Possible Sources
The various Van Richten guides
These books often detailed giving levels to NPC undead, as well as detailing the specific mechanics on how to become a free-willed member of the undying. The fluff here can certainly be used with the rules above. And even though the rules a supposed to be for NPCs, they work with PCs as well.
Unfortunately, except for the vampire, the guides focus on the big undead that you do not want to explore.
The Apocalypse Stone
This adventure contains details on how to make Death Knight PCs, including variations if you are not a warrior, like the death Warlock from transformed Wizards. (pg 93)
In the Lichland section (pg 63) Reverse Dungeon half-heartedly hints at how one might run Undead PCs. The main mechanic here is the use of HD advancement, which morphs into ELs in 3.x.
Simulating undead advancement is not necessary within the context of this adventure, since this is the last section. However, should DMs wish to continue playing a monster-oriented game after the conclusion of Reverse Dungeon,
advancement options are possible