10mm LED

The long pin is soldered to the (red) positive wire. The other end of the red wire is soldered to copper tape. The piece of copper is tapped to the postive side of the coin cell battery. 

The short pin is soldered to a shorter (blue) negative wire.  The other end is soldered to the tactile button.

6mm Tactile Button

A longer (blue) negative wire is soldered to another one of the leads on the button. The short (blue) wire is soldered to lead on the button. The two wires on the button should be diagonally apart.

LIR2450 Coin Cell Battery

Copper tape has an adhesive backing, peel a small portion and stick it on the positive and negative side of the coin cell battery. Leave some of the backing on so the copper doesn’t touch the side of the battery.