There is no ion transportation in the electrodes; such transportation takes place in the solution of ionized electrolytes, where electrodes are placed. In the electrodes, charge is transported by electrons. At best, ionic motion in the electrodes is a diffusive process, which is very slow. For the particular case of Lithium-ion battery, see the following Wikipedia entry:
http://en.wikipedia.org/wiki/Lithium-ion_battery
Here one reads that the electrolyte in this kind of battery is lithium salt, solved in an organic solvent.