You look for errors. /var/log/messages records the router's attempt to connect to your ISP and the events that occur during that attempt.
As to what you do to initiate dialing, first download the e-smith manual in PDF format and read how to set up networking in Windows. You really do nothing to initiate the connection other than open a browser, or a mail client, etc. You have to set the IP for the e-smith server as your default gateway to the Internet -- and you do this on your Windows machines. Any time the Windows machine needs to connect to the Internet, E-smith takes care of it for you.
Download the manual, it's a quick read and should answer this to your satisfaction. Odds are, your e-smith machine is working fine and the workstations simply need to be configured.