How is goiter managed?

Variable. Goiter simply means a growth in the thyroid. Three things: 1) what are your thyroid function tests? Hyperthyroidism is managed differently from goiters with normal or low function. 2) usually an ultrasound is done to look for nodules suspicious for cancer - with biopsy if needed, 3) goiters are sometimes removed if they are enlarging significantly or cause swallowing or breathing issues.
Goiter. Trying to discern cause. Lab tests including function, antibodies, tumor markers. Scans like ultrasound or radio iodine uptake.
Depends. If there are nodules that are suspicious for cancer, surgery will be indicated to provide final diagnosis and definitive treatment. If not, you may be able to manage this with medication. Your healthcare provider should talk to you about the options including whether you should also consult with an endocrinologist.