These muscles which are all named for their origins and insertions all end in -glossus which means they all insert into the tongue. These muscles do not change the shape of the tongue like the intrinsic muscle but instead change its position. These muscles like the rest of the tongue muscles discussed in this section are innervated by fibers derived from the hypoglossal nerve (cranial nerve XII). Remember we already discussed one of the muscles, the palatoglossus with the muscles of the palate and will not discuss it here but one should understand that it is considered one the extrinsic muscles of the tongue too.
The genioglossus starts at the genial tubercles which are found centrally in the inferior portion of the deep surface of the mandible. It inserts into the hyoid bone and fans out to insert along the base of the tongue. As the insertion is over a long area and the relationship of the hyoid to the genial tubercle varies over that area, the action depends on which area of the muscle is contracted. Contracting the superior portion will bring the tip of the tongue towards the floor of the mouth in an inferior and posterior direction. The middle fibers will depress the entire tongue and the inferior fibers which are attached mainly to the hyoid bone will draw the hyoid anteriorly and in consequence will protrude the tongue.
The hyoglossus muscle originates along the anterior portion of the hyoid bone from the greater cornu to the midline. The insertion which unlike the genioglossus is similar in length to the origin is along the lateral portion of the tongue. It acts to depress and retract the tongue. This is the main connection between the hyoid bone and the tongue.
As I am sure you expect by now the styloglossus muscle originates at the styloid process and inserts in the tongue. In fact, its fibers join the inferior longitudinal muscle and the hyoglossus muscle. This muscle will, due to its position, elevate and retract the tongue which is important in moving the bolus of food into the esophagus.