1. Get a substrate
2. Plan a background 
3. Plan a method of wall attachment
4. Apply the background
5. Draw traces
6. Apply metallic tape
7. Affix wire to substrate
8. Affix wire to receiver
9. Test/Finalize

This can be anything semi rigid. For 87-108 MHz, the antenna needs to be 28x34" which is λ/4 of the min and max in the range. I elected for a 1" border, which brings the final size to 30"x36". This is big. A stretched canvass would be nice, but will be expensive because of the size (both odd and big). I used 1/4" plywood, and while nice, it was a little too warpy, especially without a primer on the back. 1" insulation might have been a good pick, but attchament mechanisms might fail. Paper could work, if you put it in a frame, but then you would need to figure out how to get the wires inside the frame, and finding a non-custom frame that size will be a challenge.

Use your artistic instincts. If not, just buy/print a big poster.

30"x36" is big. It needs to fit somewhere upright and attach by wire to where your receiver is. You need to plan where it will go, and how it will affix to the wall. This can be as simple as putting the tape straight on your wall. However, if you look at my painting, the two bolts at the top are there to add the hanging wire in the back...because I neglected this step at this stage.

Whatever that means to you. I spray-painted wood. If you are doing this:

1. Prime both the back and front. Wood absorbs water form the air. I neglected this step, and when I open the windows, my antenna warps 4" off of the wall.
2. For shadow painting, see: http://www.rainbarrelparts.com/learn_how_to_paint.php, for space painting, see: https://www.google.com/search?q=spray+paint+space+art&tbm=vid
3. Make sure your edges are painted, you will regret it otherwise.
4. You need a smoothish surface. For wood, this required varnishing, sanding, varnishing, sanding, varnishing.

The patent says that 2 iterations of the fractal is ideal. This means that you will be applying the shape that I did exactly. Unless you want to go to the patent and try to figure out another iteration 2 fractal that you want to try.

You do have a choice whether to follow the patent's anti-shorting scheme or mine. The patent has gaps at the corners, which allow it to be PCB etched in one layer. I am applying tape, and wanted to cut as few pieces as possible, so I cut long strips, and then where there were intersections, I applied transparent paint sufficient to insulate one layer from another.

I drew the lines with a dry erase marker, which comes off of polyurethane with rubbing alcohol, and a ruler.
I drew a 3x3 grid, and then erased 4 of the outer lines with an alcohol swab. I then made a 3x3 template for the internal ones, and then copied that to the 5 places with iteration 2. I then again erased the unneeded lines with an alcohol swab.

1. I applied the longest horizontal strips first. Then I painted with transparent layers of acrylic over each place where an ink line crossed a copper strip. Suggestion, make the dots big (~1"), and put down 2-4 thin layers of acrylic, this will reduce the chances that you will have to find and repair a short later. If the thing is shorted, you wont get the full benefits of the fractal antenna (whatever that means).
2. After applying the long horozontal strips, apply the long vertical strips.
3. Check with a ohmeter that there are no shorts. I printed a figure of the patent, and then checked off each connection when it was optimal, whether that meant infinite resistance at overlaps, or <2 ohms for junctions.
4. Start applying your short junction strips. Connect the middle section last. I was looking for 1.2-1.8 ohms for each junction, if it was higher than that, I would press down the tape a little harder, and maybe add so more tape layers to beef up the connection. When I had all 4 corners done, each segment loop was around 17-40 ohms.

1. Plan where you want to open the loop. I picked a corner. The patent picked the middle. I can think of no reason it matters, but I am a physicist, lawyer and artist, not an analog engineer.
2. Open the loop where you want.
3. I reinforced the place where the wires would connect.
4. I drilled a hole in the reinforced area, I then put my bolts, washers and nuts so that I had (from front to back):
   1. Bolt head
   2. washer
   3. copper tape
   4. substrate
   5. wires to receiver
   6. washer
   7. nut

1. I took the wire, snaked it to the receiver, and twisted the ends.
2. Because I have one of those unthreaded coaxial FM inputs, I simply stuffed one end in the inner hole, and taped the other to the outer metal lead. I then wrapped electrical tape around both, to create a permenant-ish un-shorted connection.

You are at hackaday.io, you know how to do this. This also involves the peculiarities of your receiver. Mine didn't work immediately because in getting to the back of the receiver, I had managed to short the SPEAKER (not antenna) wires. My receiver had a failsafe where it would silently scream if this occurred, and shut off. Your mileage may vary.