This article will be broken up into different sections so you can skip around to what interests you most. I'm going to start with the Outgoing Mail server because that will be relevant to ALL email setups so you should definitely read that.
OUTGOING MAIL SERVER
In order for you to send email, you must send your email to a server that knows what to do with email. This is often called an SMTP server. It stands for "Simple Mail Transfer Protocol." It is important to remember that you must have authorization to use someone's outgoing email server. For Optimum Online users, every customer has that access. Their outgoing mail server is:
mail.optonline.net
So long as you have a cable modem, Cablevision knows that you are a paying customer and therefore lets you send mail through the above server. All others will be denied access.
If you have a MobileMe account, the outgoing mail server is filled in automatically for you because it is recognized within Apple's Mail that you are a paying customer.
Special Note:
If you have a laptop and you have Optimum Online you may have no problems sending and receiving email. But once you bring your laptop to your friends house, you might notice that you can't send email anymore. Why? Your friend may have Verizon FiOS or something like that. You can still receive mail because your application (Apple's Mail) can still reach (and check) the incoming mail server. That is never blocked. Only you have access to that account via your username and password. However, the outgoing mail server is configured to use "mail.optonline.net". This will not work at your friend's house because he doesn't have Optimum Online (or a Cablevision modem) and therefore you are denied access to the outgoing mail server.
How do you get around this?
Well, you can either use a different email account to send the email, you can logon to the web interface and send mail through a web browser or you can just wait until you're back on the appropriate network (the optonline network). Other systems use a username and password to secure their servers. Cablevision uses their own modem as the key to their network.
INCOMING MAIL SERVER
Optimum Online makes it convenient for us because their Incoming Mail Server is the same as their Outgoing Mail Server:
mail.optonline.net
If you are using a MobileMe account, this information is automatically entered for you. If you are using a Gmail account, I believe the correct incoming mail server is "pop.google.com" or "imap.google.com". Every service has their own servers so you must get this information from them. Otherwise, setting up any email client will be impossible.
USERNAME
This is usually the part of your email address before the "@" sign. That is the case for Optimum Online. For many other services, it is often your full email address.
PASSWORD
I've heard so many times from people that they don't have a password for email. That is impossible and extremely unsafe. It is just that their email client was already configured to auto-enter it and so therefore the user never had to enter it again. Please remember your password. Losing it is only going to cause you grief.
Now lets go through some screenshots so you can really see how to set it up.