After some basic research, I have come to the conclusion that the secret to looking Finnish is a) wearing spectacles, preferably with dark frames to emphasize your intelligence; b) sculpting perfect unisex haircut to avoid traditional gender stereotypes.
Don't believe me? Try here, and here, and here, and here, and also here.
That's it. It's a two-point plan. As for looking like an Estonian, just stuff a potato under each cheek. And remember to smile for the camera.