Size and count of hidden layer can be properly set only with empirical reseach. There is no technique which could produce optimal neuron count or hidden layer count.  Good rule of thumb is to perform crossvalidation and test/evaluate model on outsample data.

The more data for training you have, the bigger size of hidden layer can be. Try to divide training dataset length by connections count. If you have more than 300 you are on good path to success.

I think the determination of hidden layer number and size should be based upon the trainning performance of ANN, and some optimization algorithms need to be used to seek for the suitable number and size that corresponds to the mimimum error.

The tiling algorithm, http://lptms.u-psud.fr/membres/Mezard/Pdf/89_MN_JPA.pdf might be a good place to start. Cf. also http://www.phys.ens.fr/~monasson/Articles/a02.pdf

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.117.8327&rep=rep1&type=pdf

and references therein.

There is a theory on the subject and it is useful to learn it. 

Absent any discussion of what the properties of the association to be learned are, the question doesn't make sense. A given architecture cannot represent certain associations, so it's meaningless to try. 

I usually follow this criteria:

In the design phase, first we use the hyper-parameters (filter size, number of filters and stride which collectively decide the number of neurons inside a layer), I use the hyper- parameters used in another proven algorithm in the field ( image recognition in my case), then tune the network putting in mind one design constraint that is we need to start from a relatively big filter size reducing it as we go from lower to higher levels in the model in order to implement size invariance; i.e. the algorithm need to recognize objects in the same category despite the various sizes of its data instances