Placed after a noun to suggest an example or option ('or something', 'for instance'); often used with ～なり～なり.
コーヒーなり紅茶なり、何か飲み物をどうぞ。
Have a drink like coffee or tea.
本なりノートなり、持って来てください。
Bring something like a book or a notebook, please.
Used in the pattern ～なり～なり to present alternatives ('either A or B, do one of them').
電話するなりメールするなり、連絡してください。
Please contact me either by phone or by email.
行くなり行かないなり、早く決めてください。
Decide quickly whether you will go or not.
After a verb in dictionary form to mean 'as soon as' or 'immediately after' (Vるなり...).
ドアを開けるなり、猫が飛び出した。
As soon as he opened the door, the cat jumped out.
彼は帰宅するなり、すぐに寝てしまった。
He fell asleep as soon as he got home.
After a verb in past tense (Vたなり) to indicate that the previous state continued unchanged or that the action led to a continuing state.
彼は仕事を辞めたなり、そのまま田舎へ帰ってしまった。
He quit his job and then went back to the countryside (remaining in that state/action).
彼女は電話を切ったなり、誰にも連絡しなかった。
After hanging up the phone, she didn't contact anyone (and the state persisted).