how do i change iCloud account on iPhone 4s

Go to Settings > iCloud and tap the "delete account" button. Then sign in with the new account.

You must go to Settings, "iCloud" section". In the iCloud section (in the left column) you'll see an "Account" element (in the right column). You should tap that element and change Apple ID and password with new one.

Settings>iCloud...scroll down...Delete Account.

Settings>Mail, Contacts, Calendars.

Select the account.

Change the information as required or delete the iCloud account and set up the new one.

Is this going to "destroy" the existing iCloud account and all data that is stored in there? I have the same apple ID signed in at two devices, I want to sign one device out and sign in different Apple ID, meanwhile the original Apple ID should remain on the second device. Will I be able to use the old iCloud account on the second device with all data or it will be erased?

As far as I know the data will be removed.

Apple ID element is greyed out. I cannot change it.

I cannot change this account. It needs the code of the existing old account, which I do not have anymore. If I want to elimenate the account it telles me that I should put in the code.

If the "old account" is, in fact, yours, then you need to go to https://iforgot.apple.com and reset the password.

If it is NOT yours, you will need to get the account owner to remove it. If you do not do so, and you update or restore the phone, activation lock will kick in and the phone will be a brick.