You can add passwords to the iCloud Keychain by visiting the website in Safari and signing into the account when it prompts you for the Username & Password. If you have Keychain enabled in Settings > iCloud, Safari will prompt you to remember or update the password.
If you are not getting this prompt, go to Settings > Safari > Passwords & Autofill > Saved Passwords and use the Edit option to delete any current entries for the website you are trying to add. Also, check Settings > Safari > Passwords & Autofill > Names and Password and ensure it is turned on.
One thing to note is that iCloud Keychain is only accessible from the Safari App, so it will not autofill you usernames or passwords to any other apps including another browser. Also, the webpage must display both a username and password field in order for the autofill to work properly.
One example is if you go to gmail.com via Safari and log in, the first time it will have both blanks. If you choose the option to remember you, then it will only display the password field from then on, therefore autofill will not work. You must Delete Cookies in Settings > Safari to get rid of the 'Remember Me' setting for that website, then log in again and do not choose 'Remember Me'. This will make the website always give you both fields and allow iCloud Keychain to fill properly.