Once you reopen ACT! after installing the Click Dialer Plugin for ACT!, you'll see that your phone fields now have a new button next to them.
Note that the buttons may appear on top of other fields (like the extension field which is typically to the right of the phone field). You may need to adjust your layout to move these fields out of the way. You may also adjust the positioning of the buttons, see the Advanced Options topic.
To call one of these numbers, simply click the button next to it. Your dialer will popup and make the call.