First confirm that all the components are included:
1 2032 Battery, 1 Metal Battery Clip, 1 LED, 1 90° Degree LED Holder, 1 Button, 1 Resistor

Take the battery clip and place in the in the shown orientation

Flip the board, it helps to place the battery as a stand to help hold the board up. take the legs sticking through the board and bend them flat, this will hold the battery clip in place. Then solder them.

Place the button into the switch slot, make sure the button is oriented correctly. Give the button a push it will lock its self to the board.

Flip and solder.

Bend the resistor like this

Place it resistor spot

Take the legs and pull apart them apart to lock the resistor in its position. Then solder.

Take the flush cutters and trim the resistors.

Last up is the LED

Take the plastic 90 degree holder and put the LED through as demonstrated. Make sure the short leg is on the correct side.

Double check that the short leg of the LED is in the “C” hole which stands for cathode. Then spread the legs to lock the LED into the position and solder.

Trim the excess legs with flush trimmers.

This is what the completed flashlight should look like.

If any legs are pieces are sticking up or if you feel any points, you can come back and trim them down. Then re solder to make them rounded.

Unfortunately most of the batteries that come with the kits are wrapped in an extra layer of plastic.
The best way to get the battery is to use the included clippers to cut around the top of the battery.