Finoha does not have a login screen in the usual sense, and there is no password.
Opening the app logs you in. The first time you visit, Finoha creates an account for you automatically so you can start learning immediately, without a signup form. That account then lives in the browser you are using.
Adding your email address — under Settings → Email — attaches that automatic account to you. You will receive a confirmation link; open it, and from then on your progress is tied to your email rather than to one browser.
To get back into your account on a new device or browser: use the email confirmation link we send you. We will email you a sign-in link; opening it brings your account across.
There is no password to remember, and none to lose.
If you have never added an email address, there is no way to reach that account from another device. Nothing links it to you. This is the single most important thing to know about Finoha accounts — see Why is there no "Log out" button? and My progress has disappeared.