This section is from the book "Applied Anatomy: The Construction Of The Human Body", by Gwilym G. Davis. Also available from Amazon: Applied anatomy: The construction of the human body.
There are three sets of veins, a superior, a middle, and an inferior thyroid, and, as Kocher has pointed out, an accessory thyroid between the middle and inferior ones. The veins ramify under the capsule and form a plexus, which in goitre is much enlarged and communicates freely across the median line at the upper and lower portions of the isthmus. The superior and middle thyroids pass outward to empty into the internal jugular. Still lower is the accessory inferior thyroid, which may empty into the internal jugular, as do the two above it, or it may pass down, as does the inferior thyroid vein, and empty into the innominate. The inferior thyroid vein does not follow the artery of the same name but with its fellow of the opposite side passes directly downward in front of the trachea to empty into the innominate vein. Its importance in operations on the trachea has already been alluded to in speaking of tracheotomy.
In removing the gland the superior thyroid artery is found at the upper outer angle, the ligature should be placed sufficiently far out to include the branch to the posterior surface of the gland. In ligating the inferior thyroid arteries they are to be sought at the lower portion of the sides of the gland and are to be ligated either close to the gland or isolated by pulling the carotid artery outward, and tied as they make the bend at the edge of the anterior scalene muscle. Between these two points lies the recurrent laryngeal nerve, usually behind the artery. Halsted advises that each separate branch be ligated as it enters the gland to avoid those supplying the parathyroids. The gland is covered by the omohyoid, sternohyoid, and sternothyroid muscles. If these cannot be drawn aside they should be divided near their upper ends in the same manner as already advised in the case of division of the Sternomastoid in removing tuberculous nodes. The sternomastoid muscle will have to be drawn outward.
The internal jugular vein often overlaps the common carotid artery, reaching sometimes even to its inner side, so that the position of the artery is not a sure guide to the location of this vein.
When a goitre dips behind the sternum the presence of the left innominate vein should not be forgotten.