You cannot open a new iCloud account on a pre-Lion Mac. If you are setting up an existing iCloud account on a Tiger Mac you will probably need to set up your email to the new iCloud server settings manually in any email application - this tutorial shows you how to enter your iCloud account settings in Apple Mail.
If you need to change the server settings and you still have a MobileMe account set up, go to to Mail>Preferences>Accounts and select it. Click the '-' button at bottom left to delete it.
Now click the '+' button to create a new account. Select IMAP as the Account Type, give it a description, and enter your name and @me.com or @icloud.com email address (you will have only the latter on a newly created account).
Click 'Create'. Enter the server address, your username (i.e. your iCloud login), and password.
Apple are now requiring app-specific password for third-party applications to access iCloud. Since Mail on Snow Leopard and earlier was not intended to access iCloud you will have to generate a password for it, for which you need to set up two-factor, or failing that two-step authentication, then you can set up an app-specific password.
In the next pane, enter the SMTP server address, click 'Use Authentication' and enter your username and password again. With both servers Mail will contact the server to check that it can connect, and this may take some time.
Finish creating the account. Now click on it in the sidebar of Mail>Preferences>Accounts. Click the 'Server Settings' button. In the pane which opens, click 'Use Secure Sockets Layer (SSL)' and change the Server port to 587. Click OK.
Your account is now set up and should work normally. It's possible that you get have 'wrong password' errors: if so you should go to http://appleid.apple.com and change your password, making sure that it complies with Apple's requirements: at least eight characters, of which at least one must be a numeral and one a capital letter; the longer and more complex the better.
© Roger Wilmut. This site is not associated with Apple.