Apple Mail is very straightforward to set up and use. Apple provides convenient guides that step you through the process for creating accounts. Apple also provides a few troubleshooting guides designed to help you when something isn't working.
The three main assistants for diagnosing problems are the Activity window, the Connection Doctor, and Mail logs.
The Activity window, available by selecting Window, Activity from the Apple Mail menu bar, displays the status when sending or receiving mail for each mail account you have. It's a quick way to see what may be going on, such as a SMTP (Simple Mail Transfer Protocol) server refusing connections, a wrong password, or simple timeouts because the mail server can't be reached.
The Activity window doesn't offer any method for correcting problems, but its status messages will alert you when something is going wrong with your mail service, and usually help you figure out what it is. If the Activity window shows problems with one or more of your Mail accounts, you'll want to try the two additional troubleshooting aids provided by Apple.