Things you'll need:

Mint Tin (I'm using the Eclipse Mint Tin here)
LEDs x 2 (Depending on the size of your mint tin)
Switch
Wires
3V button battery
Button battery holder
Drill
Soldering iron and solder
Scissors
Clipper (optional)
Plier (optional)
Hot-glue gun (optional)
White paper
Electrical tape

Step 1: Marking

Dot the stars of your chosen constellation on the tin using a marker. You can print out a template, but I decided to draw The Big Dipper by myself. Also, mark the place where you want to place your switch.

Step 2: Drilling

Drill the holes. The clipper and plier might come in handy.

Step 3: Soldering

First, solder two red wires together. Repeat for the black wires (or whatever colour you use). Then, solder the wires to the positive (longer leg) and the negative (shorter leg) of the LEDs as shown in the photo. After that, solder the positive wire to the outer leg of the 3-legged switch. Solder another wire to the middle leg.

Step 4: More Soldering

Solder the black (negative) wire to the negative side of the battery holder and the red (positive) wire to the positive side.

Step 5: Insulating

I tried sticking electrical tape onto the tin, but the stars ended up looking like red giants. So, to avoid this, wrap only the exposed parts with tape. (If you're using white electrical tape, you can probably just stick them on the tin).

Step 6: Hot-glueing (optional)

Since the hole I drilled for the switch is a little too big (in order to insert the switch from inside the tin), I'll have to use some hot-glue to secure it.