More and more tech-savvy home admins want to run their own e-mail server. Although the technology needed is not very simplistic, there are some options available.
One approach is to use pre-configured e-mail server suites which are easier to install (E-Mail Server Suites Experience Report) or you can do a manual install of the individual mail server components . But in either case it is not a good idea to run your own productive e-mail server from home. It may be feasible for simple testing, but not for proper use. For a productive e-mail server you normally want to have reliable 24/7 availability and do not want to miss e-mails, neither the ones you send, nor the ones you receive.
The main reason against running an e-mail server from home is that you normally only have a consumer internet connection with a dynamic IP address. Having a dynamic IP address means that it changes at certain points in time, e.g. when your router reconnects or whenever your internet provides thinks it's appropriate to assign a new IP address now.
And these dynamic IP addresses from the consumer pool of a provider are normally blocked and not accepted by e-mail providers. When you send an e-mail to somebody who has his e-mail address with an professional e-mail provide it is very probable that your e-mail gets rejected immediately and does not even make it into the recipient's spam folder. The reason is that too many spam is sent from consumer IP addresses either from malware infested computers or from spam e-mail servers run at consumer connections. Hence, almost all e-mail providers do not accept e-mails coming from e-mail servers running on a consumer IP connection. In addition to block certain address pools, e-mail providers normally also check if the sending e-mail server's IP address has a valid reverse-DNS-record (PTR-Record).
If you really want to run a private e-mail server from home, you can use a professional business internet connection with a static IP address. But these are normally quite expensive.
The more reasonable option is to rent a reliable virtual private server (What is a Virtual Private Server (VPS)?) in a professional data center.