What is the procedure for removing all my teeth for dentures and how do teeth below gum line get pulled?

Full mouth ext's. The procedure is called full mouth extractions, and can be accomplished in phases or all at once, depending on the treatment plan of your dentist. Broken teeth below the gum will be surgically exposed to be visualized and teased out of the bone with a surgical instrument.
Depends. Teeth and roots are removed surgically out of their sockets through a series of loosening procedures, they are not 'pulled'. The surgeon will get you numb, remove the teeth and bone, smooth the bone so that when healed your gums will be smooth and not sharp. Usually, the surgeon will then suture your gums closed and then allow time for the gums to heal prior to the final dentures being constructed.
Gently . Teeth can be removed gently and a traumatically . The procedure can be done with just local anesthetic or if you would prefer under sedation. You will be surprised at how painless it is. Visit an oral maxillofacial surgeon along with a prosthodontist. Together you will get the best result.
Complete extraction. Usually the back teeth are extracted first. After they heal impressions are made and finally the front teeth are extracted and the denture is inserted at the time of extracting the front teeth. Teeth broken below the gum line are removed using special instruments designed for grasping broken remnants of teeth. Removing badly broken teeth isn't a problem for people skilled in the procedure.
Flap raise, extract. A flap should be raised since not only it facilitates the extraction, but it is also necessary to contour the bone to prepare for the better denture adaptation. The healing is better. The ridge shape is better. The denture should look nicer and fit much better doing this way.