"Conjugated polymers like polyacetylene have alternating single and double bonds along the backbone. Translating double bonds forward by one unit results in an identical structure. The position of double bonds represents a broken symmetry. By doing this translating, one has transported an electron in each double bond one step along the chain. This requires doping, the removal or addition of a small fraction of the electrons.
This is a huge question - and there is no straight forward answer.
Start with understanding pi conjugation and how the conjugation length influences the HOMO-LUMO band gap and band widths. Homologous Oligomeric series are always very instructive in understanding this (eg Oligoacenes) The conjugation length and bandgap can be limited by the chemical structure (eg compare Oligoacenes with OligoPhenyls) , intrinsic electron phonon coupling or structural/macroscopic defects. "Conduction" is usually induced by chemical doping.
As mentioned in the previous notes, the explanation of the conduction i polyconjugated systems is based on the "band picture". The HOMO-LUMO gap decerases with increasing number of conjugated centers. In principle it should converge to zero, but the Peierls-distortion (a spontaneous alternation of the bond lengths) prevents it. If, however, the system is doped to p or n state, the system becomes conducitve.
The link below will give an "easy to read" 7 pages article about conducting polymers. I think it answers the question when it explains charge storage, charge transport, and stability . Quote:(...doping of a conjugated polymer with bromine. Bromine it too powerful an oxidant and adds across the double bonds to form sp3 carbons.).