What are the steps to identify a dark matter candidate? By looking at the Lagrangian of a simple particle physics model, how do people identify the dark matter (DM) candidates, if any? 
One of the criteria is to check whether the electric charge of the suspected candidate zero. But that is not sufficient.
What are the steps to identify a DM candidate? An explanation with the help of a simple model of DM will be helpful.
 A: 
What are the steps to identify a DM candidate? An explanation with the help of a simple model of DM will be helpful.

The requirements for a particle or particle species to be responsible for the dark matter needed to fit cosmic observations to gravitational models are that they will not contribute electromagnetic radiation in the detectable spectra, i.e. visible, xray and gammas in a strength to be seen in our detectors. 
In the standard model of particle physics there are four fundamental  interactions responsible for matter and its behavior: strong, electromagnetic, weak and gravitational. These are characterized by their coupling constant, the constant multiplying all vertices in the Feynman diagrams that are used to compute the probabilities of scatterings and decays.




The size of the coupling constants affects the probabilities of scatterings and decays for any particles. 
If a particle can interact with a strong interaction, even if it is neutral it will generate pairs of charged particles with high probability, which in the end process will generate light which would make the bulk of dark matter visible, and thus they are not candidates for dark matter.
The same is true for the electromagnetic couplings, the interactions and decays will generate light. After all that is why we see the stars, to start with, and galaxes. Because the strong forces in their core generates by the strong force (fusion) charged particles which we see as the light of stars.
The gravitational interaction is so very weak that it is out of the calculation for generating particles at this time we observe the universe.


History of the Universe 

The candidates for dark matter within the particle physics models studied up to now, have to be, at present, weakly interacting so as to survive to our days, at the far right of the plot above, and also stable enough, not to have disappeared into other visible components by now. 
In the standard model it is  only the neutrino that fulfills the requirement of weak interactions mainly and surviving to these days. Unfortunately its mass is too small to be able to generate the observed patterns , even if caught at the gravitational wells of galaxies and clusters of galaxies.
There are beyond the standard model particle models, that do have a stable ground state for  weakly interacting decaying particles . Supersymmetry (and other theoretical models) offer candidates called WIMPs, weakly interacting massive particles, with a neutral ground state particle that decays with a very small probability to standard model particles because of a quantum number conservation.
The wikipedia articles on dark matter and WIMPs explain the details. There are other models offered, not of elementary interactions which at the moment are not considered seriously, but it is an open research matter.
A: One of the way is to check the decay mode and investigate the energy of the particles to see what could be their origins and also by using conservation principle maybe you can find it. For example, neutrinos found by conservation principle in beta decay.
