疾（と）っくに, seen primarily as とっくに, is an adverb that can be translated roughly as 'long ago'. This word is an emphasized version of 疾（と）うに, a literary form which is not used much in modern Japanese.
とっくに is a sentence altering adverb, so will appear most often at the beginning of sentences, or before the verb it is describing as having happened a long time ago.

• とっくに食（た）べちゃったよ。
  I already ate.
• もうとっくに寝（ね）る時間（じかん）じゃん、まだ宿題（しゅくだい）も始（はじ）めてないのに...どうしよう。
  It is already time to sleep. I haven't even started my homework… What should I do?
• 提出（ていしゅつ）期限（きげん）はとっくに過（す）ぎているのでやってもやらなくても関係（かんけい）がない。
  The due date has long since passed, so it won't matter if I do it or not.
• 遅（おそ）いぞ！みんなはもうとっくに帰（かえ）ってるぞ！
  You are late! Everyone has already gone home ages ago!

When compared with structures like すでに and もう, とっくに will either indicate something that has happened much further in the past, or may be used simply for exaggeration.

• そんな事（こと）は言（い）われなくてもとっくに知（し）ってるよ！
  I was aware of this well in the past, so no need to tell me!