A web browser such as Google Chrome or Mozilla Firefox will ask if you want to
save your password when you successfully log in to a website like Facebook,
Gmail, etc, if you have enabled the password saving setting.
Remembering strong passwords for multiple accounts on a single website is
quite difficult and it is even more confusing if each account uses a very
different username and password for every website that you registered.
Google Chrome
Click the 3 dots at the top right corner and go to Settings. You will
see your saved usernames and passwords in Passwords.
Mozilla Firefox
Click the 3 lines at the top right corner and go to Options. Select
Privacy & Security and scroll down until you see
Logins and Passwords. You will find usernames and passwords in
Saved Logins.
In order for web browsers on another computer to show your login details, you
need to login to the browser(s) on the first computer using an account like
Gmail and it will save your data.
On the second computer and so on, login again to the same account you used for
the browser and it will sync all information that has been saved from the
previous computer.
Do not save your account login details on a public computer.