The approach we are discussing here uses Indy components - a great internet component suite comprised of popular internet protocols written in Delphi and based on blocking sockets.

The TIdSMTP (Indy) way

To send an email with attachment(s) from Delphi using Indy, we'll need two components. First, the TIdSMTOP is used to connect and communicate (send mail) with an SMTP server. Second, the TIdMessage handles storing and encoding of message(s).
When the message is constructed (TIdMessage "filled" with data), the email message is delivered to an SMTP server using the TIdSMTP.

Mail sender

As you can see from the design-time screen shot, to send an email using the TIdSMTP component, you at least need to specify the SMTP mail server (host). The message itself needs the "From", "To", "Subject", ..., and all other parts you've accustomed with.

Here's the code that handles sending one email message with attachment:

procedure TMailerForm.btnSendMailClick(Sender: TObject);
begin
  StatusMemo.Clear;

  //setup SMTP
  SMTP.Host := ledHost.Text;
  SMTP.Port := 25;

  //setup mail message
  MailMessage.From.Address := ledFrom.Text;
  MailMessage.Recipients.EMailAddresses := 
      ledTo.Text + ',' + ledCC.Text;

  MailMessage.Subject := ledSubject.Text;
  MailMessage.Body.Text := Body.Text;

  if FileExists(ledAttachment.Text) then
    TIdAttachment.Create(MailMessage.MessageParts, 
                         ledAttachment.Text);

  //send mail
  try
    try
      SMTP.Connect(1000);
      SMTP.Send(MailMessage);
    except on E:Exception do
      StatusMemo.Lines.Insert(0, 'ERROR: ' + E.Message);
    end;
  finally
    if SMTP.Connected then 
      SMTP.Disconnect;
  end;

end; (* btnSendMail Click *)

Note: inside the source code, you'll find two extra procedures - used to make the values of the "Host", "From" and "To" edit boxes persistent, using an INI file for storage.