I changed my ID Apple, how can I update my iCloud ID?

You have to sign out from iCloud and sign back in again. On a Mac, System Preferences>iCloud and click 'Sign Out'. On an iOS device, Settings>iCloud and click 'Delete account' (this will not delete the account from the server). Your synced iCloud data will disappear when you sign out but will reappear when you sign back in (give it a bit of time to do so).

I tried to follow your instructions but could not delete the icloud account because I could not turn off find my phone w/out putting in the password to the account that is already changed. I'm in a catch 22!

any resolve?

If the old ID is yours, and if your current ID was created by editing the details of this old ID (rather than being an entirely new ID), go to https://appleid.apple.com, click Manage my Apple ID and sign in with your current iCloud ID. Click edit next to the primary email account, change it back to your old email address and save the change. Then edit the name of the account to change it back to your old email address. You can now use your current password to turn off Find My iDevice, even though it prompts you for the password for your old account ID. Then save any photo stream photos that you wish to keep to your camera roll. When finished go to Settings>iCloud, tap Delete Account and choose Delete from My iDevice when prompted (your iCloud data will still be in iCloud). Next, go back to https://appleid.apple.com and change your primary email address and iCloud ID name back to the way it was. Now you can go to Settings>iCloud and sign in with your current iCloud ID and password.