Yahoo Merged E-mail Accounts Getting Unmerged

I'm assuming you mean how to access email with something other than your browser.  With a browser there's no setting up since it's just another webpage you navigate.  Examples are att and/or yahoo's webmail and gmail.

The general answer is you decide which email client app you want to use and configure it using an email service's server provider's (ESPs) settings which they would documented on their web site.  Many ESPs also have webmail interfaces as well.

Google search email client applications to see what possibilities exists for your platform (Mac, Windows, Linux, whatever).  Two of the more popular email clients that work on many platforms are Thunderbird and Outlook.  FWIW I prefer Thunderbird.  But you may need to try or research a few to see which one appeals to you in the way they present the information, e.g., the mailboxes and contents of those mailboxes.  Some have the stuff presented horizontally, or vertically, or in separate windows.  Some allow you to choose.  It's a matter of taste.

The email servers that a ESP supplies are what the client app "talks" to in order to send and receive email.  Those must be always documented by the ESP to allow their customers to configure their clients in the first place.  For att/yahoo att documents the servers here. 

Most ESPs, including att/yahoo define three server settings.  One for sending, i.e., the SMTP server and two for receiving, i.e., the POP and IMAP server.  When you define an email account (the email address, e.g., foo@att.net) to a client you decide whether to set it up as a POP account or an IMAP account.  After thet you configure the client to use the corresponding servers to access the email.

The difference between POP and IMAP is that with IMAP everything is kept on the server to allow multiple devices (e.g., a phone and a computer) to access the email in such a way that whatever you do on one device is synchronized with the other devices as well.  Delete an email on one and it's deleted on all the others that are using IMAP access.  Read an email on one and it's considered as read on all the others.  With POP each email client access is independent and in general nothing is kept on the server unless the client elects to not delete it from there (something you choose to configure).  FWIW the webmail interface supported by an ESP always mirrors what's kept on the server.

I won't go into how to do the actual configuration of the clients since obviously that depends on the client you choose.  But they all must have the server info specified one way or another.  Then there's other options which you can look up depending on which client you choose.  You can always find documentation on how to configure the client you choose.

I hope this helps get you started.  FWIW I always recommend email clients to access email over browser webmail interfaces.