Hi
The hook should be pushed out following the entry route as close as possible.
Barbed hooks tend to go in then not move and if pushed the opposite way cause less damage then trying to twist them etc as this only enlarges the entry and internal hole.
The best way to achieve this is to either use a discorger pushed down the line to the bend of the hook and then keep pushing the opposite way to the entry.
Or a pair of forceps on the bend of the hook and again push the opposite to entry.
All but the most stubborn hooks will come out neatly like this.
Big barbs sometimes stop the hook moving if embedded in cartilage and will take a bit more moving, hold the hook tight and give the back of the holding hand a sharp tap with your other hand
If the point and barb go right through to the outside cut the hook in half with a pair of cutters
Whilst I am at it I will try to explain the correct way to remove a barbed hook from ones own person.
Imagine the hook is embedded deep in the end of you left index finger,
Get a length of fishing line 60cm long; tie the two ends together so you have a continuos loop.
Put the loop over the hook and slide it down until it sits on the bend of the hook, now trap the shank of the hook with you left hand thumb tightly against your index finger,
With your right hand get hold of the loop of line and give it a quick sudden jerk or better still get someone else to do it.
I was shown this way to remove hooks by the late Fred J and was again shown in hospital when I got a size 4 single embedded in my face.
It works a treat and I have successfully removed barbed hooks as big as 8-00, painful but no long lasting problems.
Frank