I agree with Steve. I synthesized PEDOT by the following method easily. There are several methods for polymerization of PEDOT but the chemical polymerization is the best one. you can take a look in my article which published in Reactive and Functional Polymer.
The above is correct apart from only one aspect: poly-styrene-sulfonic acid (better to use this instead of its Na salt) is not for improving solubility of the monomer, but for helping to keep the PEDOT formed in dispersion (PEDOT is not soluble but forms a dispersion in water, enabled by PSS.
There are various ways to make PEDOT depending on your requirement. If you want an aqueous dispersed PEDOT, oxidative polymerization of EDOT in presence of PSS is the best route as mentioned by others. But that will give you un-wanted PSS which decreases the conductivity of PEDOT. Thought conductivity can be further enhanced by secondary doping by adding Ethylene glycol, DMSO in the dispersion or treating the PEDOT-PSS films with H2SO4.
Another interesting method is solid state polymerization of dibromo derivative of EDOT. This method is very simple and clean since the side product is only bromine which can be easily removed. But the polymer you will get is an insoluble powder.
There are other methods too for getting direct thin films of PEDOT on any substrate e. g. in-situ oxidative polymerization (using ferric tosylate as oxidant and imidazole as retarder) and vapour phase polymerization.
Electrochemical polymerization of EDOT monomers is a easy way to obtain PEDOT films. The easiest is to electropolimerize EDOT in situ by applying a 3V potential bias.