How to open the phone dialer?

Are you testing in the iOS Simulator? if so, you must test in a device.
For Android, you can test in either the Emulator or a device.

The following worked for me in an iOS device:

• <a href="tel:+1-800-555-1234">call this number</a>
  Can be invoked right from the HTML

• document.location.href = "tel:+375292771265";
  Can be invoked via a function on button tap

As for Android,

Due to security bugs in Cordova (and the fixes made to counter them), to get the above code to work, you need to open native\res\xml\config.xml and perform the following:

 - <access origin="*"/>
 + <access origin="tel:*" launch-external="true"/>