There are 4 parts required to be able to receive external mail on your Exchange 2010 server: Configuration of an external domain with your external DNS host, Configuring Exchange to accept the external domain and configuration of recipient email addresses, Adding a SMTP connector to allow email inbound from external sources, and configuration of your firewall to allow port 25 (SMTP) to send and receive mail. If you have alredy done some of these steps, please bear with me.
1. Configuration of an external domain and configuration of external DNS mail records.
First, you need to have an external domain name registered in order to receive mail from outside persons. You mentioned you have an internal ".local" domain; let's call this "domain.local". An external domain name could be "domain.com", "domain.net" etc... If you don't have one of these already, I would suggest NetworkSolutions.com, godaddy.com, or dyndns.org to register your domain. After you have selected and registered your domain, you need to choose an authoratitve DNS provider to hold your DNS records for your new external domain name. I believe the three companies I listed also offer DNS services such as DynDNS.org's Custom DNS service. This will allow you to create Host (A) records and Mail Exchange (MX) records required to properly route mail to your server externally. You will need to create two records; the first being a host (A) record for your mail server. This relates your domain to your mail server's IP address, the record will look like this: "domain.com A 35.46.77.445". Now that the world knows which IP address your server sits behind, you need to tell DNS how to route mail send requests. This requires a Mail Exchange (MX) record. These records contain a priority allowing multiple to be created for redundancy and availability. The MX record should be formatted like this: "priority MailDomain MX Mailhost" and should look like this: "10 domain.com MX domain.com". After these two records are created, it's time to setup Exchange.
2. Configuring Exchange to accept the external domain and configuration of recipient email addresses
Enter the Exchange Management Console on the server and browse to: "Organization Configuration/HubTransport" and click on the "Accepted Domains" tab at the top. In the "Actions" pane on the right, click on "New Accepted Domain". When the wizard comes up, type in a name for your external domain then add your "Accepted Domain" value (ie: domain.com), then click "New". You may choose to make this new domain the default or not. If you intend this server to regularly send and receive external mail, I would make this the default domain.
Browse to: "Recipient Configuration/Mailbox" right click on a user who will receive external mail and click "Properties". Select the "Email Addresses" tab at the top and review the list of email addresses listed. If there is no email address listed for your external domain then choose "Add". Type in their external email address into the "Email Address" box (ie: user@domain.com) then click OK. Repeat this step for each external mail enabled user.
3. Adding a SMTP connector to allow email inbound from external sources
Again using the Exchange Management Console, browse to: "Server Configuration/Hub Transport" and at the bottom of the main pane you should see a section for "Receive Connectors". In order for external mail to be recieved, a connector with the following settings should be configured: "Receive mail from the following IP addresses: 0.0.0.0-255.255.255.255; TLS authentication; Anonymous Users". Review the settings of your current receive connector(s) and if you don't have one of these "generic" connectors, create one.
4. Configure your firewall forward port 25 to your mail server... I'm assuming you have this one under control.
That should do it. There is plenty of further documentation on how to do this if, for some reason, this doesn't do it.