I used this pop-up fabric coffin from the Spirit Halloween Store. It doesn't have a lot of stability and probably wouldn't support the weight of the mirror without collapsing. So the first step was to reinforce the coffin to make it sturdier.

I cut several long pieces of cardboard to the depth of the coffin (about 8"). I spray painted the cardboard black, and used gaffer's tape to tape the corners together. For the small bend in the sides, I scored the cardboard lightly and that gave me enough play to push it into the corners. 

I fit the cardboard support frame into the coffin and it added a lot of stability. It also gave me a good surface for attaching the mirror. 

Follow the directions that come with the mirror film. For mine, here were the steps I followed:

1. Clean the plexiglass thoroughly. Any specs of dust or dirt will DEFINITELY show.
2. Cut the film to size, leaving a little extra along the edges.
3. Peel the clear backing off the mirror film.
4. Mist the plexiglass with water from a spray bottle.
5. Place the mirror film adhesive-side down onto the wet plexiglass. Use a wallpaper scraper or other straight-edged tool to smooth out all the bubbles by pushing them from the center out to the edges. Take your time with this -- any bumps or dust motes or bubbles will mess up your illusion.

Once the adhesive has dried, you'll find yourself with a fairly decent 2-way mirror. 

I placed my coffin on top of the mirror and traced around it with a sharpie to get the shape of the coffin. Then I cut the mirror to size with a band saw. It fit on the first try! 

Run gaffer's tape along one side of the mirror, hanging the tape over so half of it is on the mirror and half is free. 

Place the mirror inside your coffin halfway betwen the front and the back. I propped mine up on small paint can to hold it at the right level. Stick the tape securely to the inside of the coffin. You'll want to tape both sides. I found it easiest to place the tape side down with the coffin open and reach underneath to get the tape stuck on to the back side. Then I went over the front side with more tape in the same fashion. 

Once the mirror is secure and not going anywhere, tape the lid of the coffin closed with more gaffer's tape.

Mark and cut a hole in the front fabric of the coffin using a utility knife. This is your viewing window so make it fairly big, but not so big that it shows the edges of the mirror.

Flip the cut-out pice upside down and put it on the back of your coffin, lined up with the front hole. Trace around it to get the same shape hole on the coffin back.

Add a border of gaffer's tape around the edges of the hole to define it and keep it from raveling.

Now it's time to install the lights. Reach inside the coffin and peel back a little bit of the tape holding the mirror up on one side. Thread the last two strands of LEDs through the hole so you have two strips on each side of the mirror.

Use gaffer's tape to securely tape the LED strips to the inside of the coffin around the opening. The light should be facing outwards, so they shine on the viewer (or the skeleton) standing outside the coffin.

Use enough tape that the light doesn't bleed through the back of the strips. Any stray light that escapes will get picked up by the mirror and wreck the illusion. The idea here is to isolate the light strip on the front from the one on the back, so you have only one side lit at a time.