I broke my thumb about 10 years ago, but it's still very stiff. How can I deal with this?

See your doctor... You could have tendon or joint problems related to the original injury; or have developed slowly and unrelated in that earlier injured thumb. Arthritis in the thumb is another common cause of thumb siffness but is associated with pain. See your doctor for an exam and maybe x-rays.
Begin w/hand therapy. You should see a hand surgeon to determine why you are stiff. X-rays will be needed. Unless there is an obvious surgically correctable problem, you will probably be prescribed a short course of hand therapy. Good luck.