Overview of parts included in the kit (note the CR2032 coin cell battery is not included). You'll need to get one separately.

Depanelize the PCB by carefully bending the PCB on the mouse bites.

Optionally clean the rough edges with some sand paper or a file. 

Mount the first LED on the Space Shuttle body. Pay attention to the "+" symbol indicated on the PCB, this is where the long lead of the LED goes. Do not push the LED all the way flush with the board, rather keep a little distance so you can bed the LED to the back before soldering.

Using flush cutter to trim the soldered leads. Hold the leads when cutting to prevent them flying away. Preferably you should wear eye protection during this step.

Now it's time to mount the 2 LEDs on the wing. Just like the previous LED, make sure to bend the LEDs towards the back before soldering them in place and cutting off the leads.

Next up is soldering the baseplate. Gather the base PCB, battery holder and slide switch.

Start by mounting the CR2032 battery holder. Pay attention to the arrow on the PCB indicating the chamfered edge on the battery holder. A tip for properly mounting this SMD part: start by tinning one of the pads before mounting the battery holder. Then heat up the pad and slide in the part to the correct position before removing the heat and keeping it in the right spot.

The switch is to be inserted on the same side as the battery holder. 

Assemble the Space Shuttle by sliding the stem of the body through the hole in the wings. Solder only 1 side for now! 

It's very likely the body is mounted a bit crooked on the the wings. Heat up the solder joint again while holding the Space Shuttle body and wings in the other hand. Slowly maneuver the boards in the correct position once the solder joint has heated up sufficiently. Once the orientation is to you liking, lock it down by soldering the second solder joint on the bottom. Don't be stingy with the solder on these joints!

Pay attention to the "+" markings when mounting the Space Shuttle on the base. These should line up resulting on the the LEDs pointing in the same direction as the slide switch. Use the same approach as shown in the previous step to achieve the optimal mounting angle to your liking.

Some caution is required when mounting the battery, slide it underneath the hooks on the front side with the "+" side facing up before pressing down

The only thing left to do is slide that switch to the "ON" side and marvel at your work!