How can I ask SharePoint to authenticate through external authentication services?

You need to configure it on IIS:

1.Click Start, point to All Programs, point to Administrative Tools, and then click Internet Information Services (IIS) Manager.

2.Click the plus sign (+) next to the server name that contains the virtual server you want to change.

3.Click the plus sign (+) next to Web sites.

4.Right-click the virtual server, and then click Properties.

5.On the Directory Security tab, under Authentication and access control, click Edit.

6.Select the check boxes for the authentication methods you want to enable, and clear the check boxes for the authentication methods you want to disable.

7.Click OK to close the Authentication Methods dialog box.

8.Click OK again to close the Properties dialog box.

Thanks dj0rbit.  Can you be more specific which options should I choose to enable an external authentication through a domain controller?  I followed your instructions, but I'm not sure which authentication method I should choose.  Thanks.

it would be "Anonymous" but it's not recommended because it can affect your security polices.

I'm sorry I don't understand.  Why authenticating through a domain controller would use Anonymous as its authentication method?  Please help.  Thanks.

So just to be clear, you're trying to have external users that's not on the domain connect to sharepoint?

No.  That's not what I meant.  Sorry for the confusion.

I'm trying to enable the users on another domain (that's is different from the one that my SharePoint server resides) to log into my SharePoint server using the same credential they use on their own domain.

not so good