Mailbox at your web hosting account

Send and receive mail as you@yourdomain and from as many other addresses as you want to use.
Web/email hosting accounts are relatively cheap, starting from around $40pa.

Pros

• Usually provided at no extra cost if you have a web hosting account
• Usually unlimited number of email addresses
• Mailbox quota limited only by the size of your hosting account

Cons

• A single mailserver which could be unavailable for a variety of reasons. In contrast, a mail service provider ensures multiple servers are available to process your mail
• Your reputation can be affected by other users who also have mailboxes for their domain hosted on the same server
• Reliance on the administrator of your mailserver (usually the hosting company) to maintain email policies at an appropriate level to avoid reputational damage resulting in your domain being flagged as a spammer

Setup

This varies from one hosting control panel to another, but information on how email accounts are created in cPanel can be found here