This is by no means an easy question, and there is no "standard way" to do a "basic setup" in Exchange, which is quite a complex product and definitely needs some study before deployment.
That said, the main points you should look into are:
- Accepted domains (in Organization Configuration): these are the SMTP domains your server will manage messages for. You should define at least one authoritative domain for your public DNS domain.
- E-mail address policies (in Organization Configuration): this tells Exchange how to create addresses for your users. The most basic setup here is to give each user an address in the form
- Mailboxes (in Recipient Configuration): your users will of course need one, in order to be able to actually use Exchange.
- Send connectors (in Organization Configuration): these tell Exchange how to deliver outgoing messages; you will need at least one of them, configured for delivery of Internet e-mail to external domains.
- Receive connectors (in Hub Transport server configuration): this is the SMTP server listening on your server for incoming messages; this will not by default accept incoming external e-mail, because it would want an Edge server in this role; if you want this server to directly receive e-mail from the Internet, you will need to allow anonymous connection to the default receive connector on your Hub Transport Server.
- Firewall: you will need to allow incoming SMTP traffic (TCP port 25) from one external public IP address to your server's private one, by means of NAT; and you will of course also need to let your server establish outgoing SMTP connections to external addresses.
- DNS: I assume you already did this, otherwise you will need to configure the MX record for your public DNS domain to point to the public IP address whose TCP/25 port is then forwarded to your Exchange server.
This should get basic mail flow going; then you'll have to look into the two other most important points of Exchange configuration: storage and web services; but talking about that here too would really make this answer too lenghty and complex.
I strongly suggest you read a book or two about Exchange... it's quite a complex beast. Really.