I want to ask for caution when stating "cognitive functions could be improved by anodal tDCS"! 

In my believe, this is strongly overextending most of the studies done in this context with respect to "generality". 

If you look at attached Fig 1 from  Krieg, T. D., F. S. Salinas, S. Narayana, P. T. Fox and D. J. Mogul (2013). "PET-based confirmation of orientation sensitivity of TMS-induced cortical activation in humans." Brain Stimul 6(6): 898-904. you will understand that the effectivity of (here TMS induced) electrical potentials do depend on the orientation of their field vectors relative to the neuron's orientation. 

Now, as consequence to this field/neuron-orientation, the montage location on the skalp is of utmost importance! In light of the above, the montage should be determined for each subject according to an (f)MRI map of his/her individual sulci/gyri structure (it is said, that brain wrinkles are as individual as finger prints....). The 10-20 EEG system may be used to define inter-subject comparable positions, but of course, the usual EEG-electrodes do integrate over a HUGE area of brain surface - leading to a discrepancy between functional brain structure and skalp position... Sometimes you want to record from C3 - presumably over motor cortex, yet the signals from there are poorly correlated to visible motion... Both just don't match. I do not have a reason to think that the tDCS "writing into" the motor area under C3 would show higher localization and precision.... 

So, when all of this is well controlled among subjects, the question obviously arises, which types of cells with which function are you actually reaching with your tDCS stimulation.... And that of course will determine your outcome. So, please be sceptic with general claims of "tDCS improves...". 

All the best!

uli

Sorry, I just realized, that you are actually looking for something else: How does tDCS work at all? 

It may oversimplify, but have a look at the attached figure: As soon as you are bringing a somewhat elongated neuron in an electric field in the range of 1V/m (mV/mm, very reasonable value with tDCS) you are not able to actually "make the neuron fire" (that would need way higher field strength). But the resulting polarisation will "detune" the normal firing pattern of this neuron: It may increase average firing rate or decrease it. It is called Short Term Depression/Potentiation (STDP). Now, depending of the type of cells (inhibitory or excitatory) and the direction of electric field (cathodic or anodic) the results may look different to the surrounding network - and that makes the effect to the macroscopic "cognitive" results. 

See for example: 

Froehlich, F. and D. McCormick (2010). "Endogenous electric fields may guide neocortical network activity." Neuron 67(1): 129-143.

or for tACS:

Reato, D., A. Rahman, M. Bikson and L. C. Parra (2010). "Low-intensity electrical stimulation affects network dynamics by modulating population rate and spike timing." J Neurosci 30(45): 15067-15079.

Cheers!

The concept of tDCS is based on normalizing or enhancing (military air traffic control studies) brain function. In psychology, the utility of tDCS is dependent upon neuronal activity in the area of stimulation. Anodal stimulation reduces slow wave activity and cathodal stimulation reduces (fast) beta activity. Therefore if you have focal slowing (such as TBI), anode stimulation in the center of the slowed area is the desired intervention. Likewise, in the case where you have spindling excessive beta activity in the anterior area, applying the cathode to Fz will reduce this activity and decrease anxiety. A note of warning: if the EEG identifies epiliptiform activity, tDCS is contraindicated because it has the potential to elicit a seizure. EEG should be done prior to the application of tDCS to first rule out non-convulsive seizure activity and to identify the areas of abnormal activity.

This is a very interesting question, which is just now beginning to garner the attention of researchers! Below is a study that found that cathodal stimulation prior to a working memory task produced better WM performance compared to anodal stimulation (prior to the task).

Carvalho, S., Boggio, P. S., Gonçalves, Ó. F., Vigário, A. R., Faria, M., Silva, S., … Leite, J. (2015). Transcranial direct current stimulation based metaplasticity protocols in working memory. Brain Stimulation, 8(2), 289–294. http://doi.org/10.1016/j.brs.2014.11.011

Abstract

BACKGROUND:

It has been already shown that delivering tDCS that are spaced by an interval alters its impact on motor plasticity. These effects can be explained, based on metaplasticity in which a previous modification of activity in a neuronal network can change the effects of subsequent interventions in the same network. But to date there is limited data assessing metaplasticity effects in cognitive functioning.

OBJECTIVES:

The aim of this study was to test several tDCS-based metaplasticity protocols in working memory (WM), by studying the impact of various interstimulation intervals in the performance of a 3-back task.

METHODS:

Fifteen healthy volunteers per experiment participated in this study. Experiments 1 and 2 tested an anodal tDCS-induced metaplasticity protocol (1 mA, 10 + 10') with 3 interstimulation intervals (10, 30, and 60 min). Experiment 3 determined the effects of a similar protocol-with a 10-min interval between two sessions of cathodal tDCS or anodal plus cathodal tDCS (1 mA, 10 + 10').

RESULTS:

Two consecutive sessions of anodal tDCS delivered with a 10 min interval between them did not improve WM performance (P = .095). This effect remained the same if the interval was increased to 30 or 60 min. In contrast, when a 10 min interval was given between two consecutive cathodal tDCS sessions, performance in the 3 back task increased (P = .042).

CONCLUSIONS:

These results suggest that the polarity effects of tDCS on working memory are dependent on the previous level of activity of the recruited neural population.

I hope this helps.

Nice Contribution Ronald Swatzyna