The Keychain Access will open.
Here you will see several entries with saved passwords for applications, websites, network shares and wireless networks.
If you are getting a bunch of pop-ups asking for your credentials from the Keychain Access program that won't go away.
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Try locking and unlocking the keychain. When you unlock it you will be prompted to enter your password.
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Try your current password if it works then you're done. If it doesn't work then you will have to try your previous most recent password and you will have to change the password manually (see below).
-> If you are still getting bombarded with pop-ups you might have to go about manually deleting entries.
The next time that you log into the application, website, network share or wireless network, a pop up will prompt you to enter your new password and a check box to save to Keychain Access.