[subject] + 曾经 + [verb] + 过 + [object]
[subject] + 曾经 + [verb phrase]
曾经 puts an event or a state at some point in the past and implies it's over. It goes after the subject and before the verb, and the verb usually takes 过.
It can also describe a past state that no longer holds, where English says "used to".
曾经 sounds a little more formal than plain 过, and suits storytelling and writing.
已经 says something is done by now and still matters now. 曾经 says it happened once and is in the past.
To say something has never happened, drop 曾经 and use 没(有) + verb + 过. 不曾 exists, but only in writing.