How to sign in depends on the version of Quarterfall.
Quarterfall ONE is the free version of Quarterfall. When you have an account for Quarterfall ONE, go to https://one.quarterfall.com. Here you are asked to provide your email address. You are then mailed a temporary link that you can use to sign in. This brings you to your teacher dashboard.
You can use the same page to register for a new account for free. Just type in your email address. If you do not have an account you are asked to provide your name and to accept the conditions. Press Continue. You are then mailed a temporary link to complete your registration. This brings you to your teacher dashboard.
When you have an account for Quarterfall, go to https://pro.quarterfall.com. Here you are asked to provide your email address. You are then mailed a temporary link that you can use to sign in. This brings you to your teacher dashboard. For certain institutes, you will be able to login using your institution's authentication mechanism and then use Quarterfall directly. Quarterfall knows what role you have (e.g. staff or student) so it will show you the information that is appropriate for you.
It is possible that you have an account at multiple organizations with the same email address. For example, at two departments that each have their own Quarterfall license. When you sign in you are viewing the same organization that you viewed last time. You can change the organization in the avatar menu at the top-right.
In the past you might have had a password for Quarterfall. Quarterfall no longer uses passwords but now uses the magic link mechanism described above. So you will never need that password anymore and can discard it.