There are two ways that I know of for removing a stuck hook from a body. I must warn you - the videos below are not for the squeamish or those who can't stand the sight of blood. The first video below demonstrates one method that will work with larger, longer hooks (like streamer hooks):
Obviously if the wound does not stop bleeding eventually, or if you notice anything out of the ordinary, than you need to seek medical attention. When in doubt leave the hook in the body & get medical help immediately. This is especially true if the hook is located in a place close the eye, mouth, or nose. You don't want the removal attempt to do more damage than the accident itself.
So the next time you or someone in your fishing party gets a hook in them, you'll have an idea of what to do. Just remember to be safe & when in doubt seek professional medical help.