Open Eudora, and go to the Tools | Options menu item:
Next, click on Checking Mail under the Options screen's Category panel to make sure that the Mail Server field is filled exactly as shown below, and that you type in your full email address in the User Name field (you should see something similar to this):
Now, under the Sending Mail side menu item from same Tools | Options, make sure that you fill in the form fields as shown below, taking particular care to specify the STMP Server field value exactly as shown below, and type in your full email address in the Return Address field. Finally, make sure the "Allow Authentication" box is always checked on this screen.
When you create a new installation of Eudora, you may be prompted in the setup screens to supply values for the incoming and outgoing servers, and for your user name and password. If you are not certain that you are entering the correct values, just repeat the process of "Existing Installations" above, after your installation is done, to verify and change values if necessary.