The instructions from Microsoft for enabling e-mails to be sent from a SharePoint site can be found here:
 
 
Specifically, the instructions you need are:

Using HTML Administration to Configure E-Mail Settings for Windows SharePoint Services

You use the Configure Default E-mail Server Settings page to specify e-mail settings for your server.
 
Specify e-mail settings for a server or server farm
  1. On the SharePoint Central Administration page, under Server Configuration, click Configure default e-mail server settings.
  2. In the Outbound SMTP server box, type the name of the SMTP mail server to use for sending messages.
  3. In the From e-mail address box, type the e-mail address to send e-mail messages from.
  4. This address appears in the From box of any e-mail messages from the server. No e-mail messages are sent to this address, so you can use an unmonitored e-mail address if you want.
    In the Reply-to e-mail address box, type the e-mail address that users can reply to. If a user replies to an e-mail message from the server, it will be sent to this address. You should use an address that is monitored for the reply-to address.
  5. In the Character set box, select the character set to use.
  6. Click OK. 
NB To get to the SharePoint Central Administration, remote desktop to the server, then go to Start > Settings > Control Panel > Administrative Tools, and there should be a link to SharePoint Central Administration.
 
You may wish to setup a new e-mail alias address of SharePoint@yourdomain.com for the FROM and REPLY-TO addresses - which needs to go to someone who is responsible for the administration of SharePoint (for example, they will get e-mails if people request access to a particular area for example).
 
To test if the e-mails are working correctly, go to:
 
 
And login with Adminstrative privileges. Click "Site Settings", "Manage Users" and then "Add Users". Enter a new user account (you can actually add an existing one such as "DOMAIN\yourlogin" as a test).
 
Tick the box "Send the following e-mail to let these users know they've been added". Click "Finish".
 
It will then prompt you if there is still a problem sending e-mails:
 
"The user or users have been added successfully, but there was an error in sending the e-mail message. The server may not be set up correctly to send e-mail. To verify that e-mail is configured correctly, contact your server administrator."