Instructions
Buy nothing for the Neopet. Neopets enjoy new clothes and toys. Forget buying Neocash and simply let the virtual pet go without new stuff.
Forgo food for the pet. A Neopet will not die without food, but it will become very unhappy.
Ignore the Neopet for as long as possible. Sign into the account and do nothing with the pet. Messages including "you do not play with me enough" will begin to appear when a level of neglect is obtained. Neopets do not like to be ignored.
Send the Neopet to the Battledome often. After refusing to feed or buy toys and a period of neglect, begin sending the Neopet to the Battledome often. Getting covered in slime while hungry and unhappy will send the Neopet to a depth of depression from which it might not recover.