You want to setup an MX record with the people that are hosting your DNS settings. The MX record is the IP address of the place you want email from your domain sent to. For example, you have registered your email domain with register.com, go to that website and manage your domain. Add a DNS record of mail.{yourdomain}.com (ie mail.microsoft.com) to be the static IP address the ISP has supplied you with. Then, add an MX record so that your email is sent to mail.{yourdomain}.com, at priority 1. Remember to open port 25 in your firewall, and point it to your Exchange server.

For sending, lots of ISP’s require that all outgoing email be sent through their SMTP servers. If your ISP does this, then you will need to setup and SMTP connector, which will force all outbound emails through your ISP’s SMTP server. You do this in Exchange System Manager, right click on Connectors, and click New-SMTP connector…and fill in the fields.