I have battled with an underactive thyroid for years (diagnosed in my early 30's) and have gained weight as a result. I can tell you losing weight is tricky, not like these young people where they hit the gym and adjust their diet and they lose weight. I'm nearly 50, so maybe it also has something to do with my age (women over 40 our hormones go haywire), but I've found a few sources of helpful information that I've implemented and since January of this year, I've seen the weight drop off.
First, even if you are taking meds for your unbderactive thryoid, that isn't enough. I do believe you can enhance it's function through diet. The key thing that worked for me was balancing my diet (nearly eliminated all refined carbs, sugars and replaced them with veggies and good proteins, fats). I keep my net carbs to 100-125g daily (before I was close to 200-300 g daily).
In January, I heard that people with a thyroid disorder should follow the leptin diet--esentially eat to allow leptin to do its thing. Leptin is one of the hormones in your body which help regulate body fat. Here's one of the articles that I found which sums it up nicely. The video at the end is very helpful too (and entertaining).http://wellnessmama.com/5356/cravings-fix-your-leptin/
Shortly after that, I saw this Dr. Oz episode on balancing your hormones naturally and I began to think that following these tips could also help my thyroid function. It's 5 segments long but quick to watch. I swear since doing these the weight has been coming off and I feel great.http://www.doctoroz.com/episode/melt-fat-fast-how-reset-your-secret-fat-loss-hormones?video=15580
I think weightloss is one of those things that you have to try a few things before you find what works for you.