Today, the primary use of a weapon like this is to help maintain pacifist conduct. Another possible use is to split a pudding pet before polymorphing it.
Historically, a poor iron weapon was used to split black and brown puddings in pudding farming (hence its name) while doing minimum damage: it might eventually kill a pudding, but it would split a lot of them first.
Prior to version 3.6.1, a Puddingbane could probably have been used to kill Vlad the Impaler (as a makeshift Vladbane).
A puddingbane can be created by engraving with an iron weapon to reduce its enchantment to -3. An enchantment of less than -3 is not needed for a dagger or knife, but a stronger or blunt weapon would require some cursed scrolls of enchant weapon.
Any non-weapon iron item, such as a key, will do d2 damage (or at least 1 if corroded), plus any bonus from strength of 16 or more or from rings of increase damage. Note that for pacifism, this is not as good as a -3 dagger or knife, which will always do 1 point of damage no matter what your damage bonus. Wielding a non-weapon item will preserve weaponless conduct, however.
In slashem, a Puddingbane can still be used for some very limited pudding farming.