Is there a common template or mnemonic for a take-off briefing?
I have never used any checklist or Mnemonic for this, but I do use it as a sneaky way to make myself look professional to my passengers while really using it to remind myself what the hell I'm actually meant to be doing. 

Typically it will contain the following


What will happen in the next 5 minutes ("We'll line up on the runway when told to.... we will begin rolling..... we will lift off at about [speed]")
What will happen immediately after take off ("We will climb until X, at which point I will turn [left|right] and head towards Y")
What the intention of the flight is ("We will continue via X &amp; Y to Z")
Any quick emergency procedures which might be necessary (Much like your instructor demonstrated, along with briefly what the passenger should do in case of this emergency.)


I do this at the hold when with an instructor, or experienced pilot in the other seat. If its an inexperienced or nervous flyer I take longer about it, usually sitting in the aircraft prior to startup.