How does get rid of the excess fat over my abdomen and ribs when I have severe hypothyroidism?

Correcting low T4. Correcting your hypothyroidi should be the first step towards improving your physique. Keep in mind that if indeed your hypothyroidism is profound, your body will have significant water retention giving the appearance of "puffy face" and swollen tissues. This will reolve overtime with treatment and improved thyroid levels.
Diet and exercise. Anyone with hypothyroidism should be checked regularly to make sure they are taking the correct amount of thyroid hormone. Once that is done, losing weight (or excess fat) is no different or more difficult than for people without thyroid disease. So reducing food intake and increasing activity are still the best way to meet your goals.