There are several components that enable you to do this. You may already have one, if you have an SMTP server installed alongside IIS - it's called CDO.Message. Please avoid using CDONTS.NewMail... it is wrought with problems, and is obsolete (it is no longer included in Windows XP or Windows Server 2003). For examples of using CDO.Message, please see Article #2339 and Article #2026.
There are also several other components available (if we missed any, let us know).
If you don't have access to CDONTS or CDO.Message, and can't install a COM object on your web server, you might consider using a stored procedure to send mail from within SQL Server. See Article #2403 for a tutorial on configuring your SQL Server for sending mail through Exchange, MAPI or an external SMTP server.