I learned to consciously control this after reading about the reflex years ago. The easiest way to "find" the muscle is to swallow slowly and pay attention to the feeling in your ear canals. Most people naturally use these muscles slightly when chewing or swallowing. I can hold it for several seconds before it starts to feel like an exertion. You'll know that you've got it when you can voluntarily hold a quivering/vibrating sensation in the ear along with external sound dampening.

It is not a substitute for earplugs around dangerous sounds and you cannot hold it for hours to block out the sound of an airplane engine. The only time I ever had a practical use for this was when I heard someone leaving a movie theater start to discuss what was obviously about to be a major spoiler with their friend as I was entering. The utility there comes purely from it being socially unacceptable to interrupt a stranger or suddenly cover your ears, while nobody else can see if you're using your tensor tympani.

I discovered that I could control it in my teens. I rather opt for earplugs - the muscle gets tired as all other muscles during use, and the amount of dampening is negligible in my case.