Generally, most patients are sent home with pain medication and calcium supplementation. You may also require thyroid hormone. Please follow the instructions your surgeon sends home with you in regards to your home medications.
Tylenol is safe in most cases but unless otherwise instructed, you should avoid NSAIDS such as aspirin, ibuprofen, or naproxen for 36-48 hours after your surgery as these medications can increase the risk of bleeding.
Whether or not you need other medications will depend on why your thyroid was removed and how much was removed.
For more information go to endocrinediseases.org:
Diseases of thyroid function
Thyroid Surgery: Recovery