First of all, get a hold on all the material necessary to begin. You'll need new material along the way. Depending on the design you choose and the material ($) at your disposition, you'll need more or less material and one or another type.

I will describe my development process to build my speakers:

1- I got hold of some magnets, I have already talked about some of my experiences in the development section.
Here you use any magnet that has the characteristic of being "anisotropic", this means that it's magnetized through it's largest dimension, these can be either ceramic ferrite/strontium magnets. The strontium ones are stronger and are better considering the fact that they can be set closer to one another without affecting their magnetic field as mucha s with other types. The danish project used 102 42mm x 7,7mm x 9mm (length, width, thickness) for the woofer and 60 50mm x 19 x 5mm for the tweeter section, thus twice the amount for a pair of speakers.
Considering the fact that magnets are cheaper if bought in large quantities, you can consider buying them together with other builders.

2- I started experimenting with common household material, kitchen plastic foil, chocolate paper as foil and cardboard as a frame, then later wood as frame and bigger membranes.

3- Once the principle was proved to work, I started getting the material for the full scale prototype.

4- Found the best place to buy wood, if you can buy the pieces cut, great, if they can also make the inner cuts, fantastic. Remember to get a piece cut to use as a transitory foot for your loudspeaker, in my case it's the definitive foot. Here come the first decisions, will you build the frame out of one solid piece, or a series of thinner plates stuck together, maybe mixing wood with some other stronger material.

5- At this moment you'll have to decide if you want to paint the design, I didn't with the prototype.

6- Go searching for the perforated iron plate and decide what thickness you want, depending on your possibilities to cut it, your budget and the sound considerations. Try to have a well perforated plate, with at least 50% air with respect to the iron. Thus you'll avoid making the speaker even less effective.

7- Find a place where they can cut the plate to you specifications, remember to get the plate cut to the size you made the holes in your wood plate, but even BETTER, get the plate cut before to your specified sizes and cut the wood plate correspondingly.
The woofer hole should be cut to the size you feel like building the speakers, just follow the dimension rule:
This gives you the trapezium form of the membrane, which helps to propagate the vibrations, eliminates the standing waves on the membrane, etc.
How these dimensions are really depends a lot on the design of your project, the width of your MDF plate, the width of your magnets, etc. In my project the magnets were not too wide, the MDF plate was very thick and the distance I wanted to place the magnets, due to their low magnetic field strength, forced me to put the magnets 2mm from the membrane, thus the iron perforated plate had to be cut to fit the woofer membrane hole.
The original danish design, due to a thin plate, to thick magnets and due to the strength of the magnets, could have the perforated plate screwed directly to the back of the MDF wood plate, this made the design easier and faster to build, less engineering involved.

8- Find the membrane material, a strong, thin, resistent plastic, unstretchable, not affected by atmospheric conditions, humidity, etc. I recommend Mylar, you may find something else, tell me about it.

9- Find the foil you'll use. I had a very hard time finding the chocolate foil paper here in Chile. I will not tell you where I found it, you won't have such a hard time. In Denmark it is sold in the Supermarket. You could go to a paper store.

10- Make experiments with your foil material, you need to determine it's resistence. Thus you'll be able to determine the length of foil you'll need to fulfill the 3-4 Ohm resistence the membrane must have. I will talk about that later.

11- The glue is a 3M product, there may be a number of competitors where you live, here in Chile it was my only option at that moment. Practice using it, it's effectivity, how much should you use, the wrist movement, etc.

12- Get the required amounts of L aluminium profiles, these you'll use to hold the metal plate with the magnets close to the membrane, if you chose a 30 mm MDF fibreboard, like I did, the magnets must be placed with the plate, closer to the membrane than those 30 mm, I wanted them to be 2 mm. from it, so the plate was placed aprox. 20 mm into the MDF board. I will show you a diagramme. The L profiles let you hold the distance constant.

The L- Profiles are also used to stretch the membrane out.

Continue the directions following the original directions