You shouldn't just ignore frequent hand tremors, right?

Lately, I feel like my hands are trembling slightly even when I am still.
I'm worried because sometimes it appears even when I'm not nervous, though I'm not sure if it's due to that.
Maybe it's because I drank too much caffeine.
Or I wonder if it could be a neurological problem.
I would like to know if I need to see a doctor if these symptoms persist.
I am also curious about which test is conducted first if I undergo the examination.