You need a computer, network connection (preferrably to the internet), and then you need to choose an MTA, whether it's sendmail which comes usually by default on every distro, postfix (recommended by me), qmail, exim and so on. Lastly a domain name, that's if you actually want people to send to this new mail server.
Get the machine ready, get it connected, register your domain name, choose which one you want (MTA), read up on their docs of the chosen one, come back here when you have more specific questions so we're not rewriting manuals and howto's that already exist..
