Using Eudora:

Step 1 - Install and start up the Eudora program
Step 2 - Select "Options" from the "Tool" menu
Step 3 - Select the "Getting Started" tab.
Step 4 - In "Real name", enter the name you wish to appear in your emails.
Step 5 - In "Return Address", enter the email address you wish to send mail from: whatever@yourdomain.com 
Step 6 - In "Mail Server (Incoming)", enter mail.yourdomain.com.
Step 7 - In "Login Name", enter the name of the account.
Step 8 - In "SMTP Server (Outgoing)", enter in mail.yourdomain.com or what your ISP provided you.
   **See below Using SMTP Server for more information** .
Step 9 - Click OK
Step 10 - Go to the "Checking Mail" tab and make sure "Save Password" is checked.
Step 11 - Click OK

SMTP server:

Per dialup session, you would need to be authenticated to use the SMTP(Outgoing Mail) server. This is to prevent spammers from gaining access to your SMTP server. Here is how you can be authenticated:

Step 1 - Get connected to the Internet
Step 2 - Start your email software.
Step 3 - Make sure there is no outgoing mail in your outbox.
Step 4 - Log into the POP server to check your email
Step 5 - Now you are authenticated and you should be able to send and receive email w/o any problems. As long as you don't quit the program and stay connected to the net, you wouldn't need to be authenticated anymore.

If your SMTP access is denied after trying the steps above, you would need to contact your ISP. It is likely that they are not allowing relay to outside SMTP server. More and more ISP's are implementing this feature to prevent spamming.

There is a very easy workaround to this. All you have to do is use your ISP's SMTP server. This does not affect how your email address appears on your outgoing emails. When recipients of your message hit the reply button, they will see your email address at your domain name.