1: Add a reference for the button you want to tap and one for the datepicker.
2: Add a control to listen for the tap event on your button.
3: Create a handler for the tap event that calls show on the datepicker reference.
Here is a link for the controller API which has a great description of how to setup refs and controls.
If you are not able to get to the solution from that feel free to post some code and I can try to help you with a more specific answer.
Good luck, Brad