Answer: 1. first you have to determine whether there is a crime, which is not obvious at all. In fact, nowadays, there is a strange confusion between the political and even moral ‘misbehaviour’ (if it were) and a real crime. Figure out, that in France, the pourparleur of freedom and human rights, the very fact of refusing to accept the Armenian genocide is considered a ‘penal crime’ (??!!) – may lead to prison.
2. Crimes vary from country to country, as a crime, objectively, is nothing but an infringement of law, and laws not the same all over. As little are proofs, or penalties. Why should this be of importance while running after some criminal for the strategy of investigation? Because the finality is to put someone into prison: thus, the first strategy is to know law and after, which proofs are accepted as such in order to put the criminal into jail or be fined.
3. After, you may proceed objectively or subjectively. Objectively means that you gather elements of proofs, that may imply other people’s sayings (with many question marks) and try to relate them to one determined subject. Usually, you have to obtain the confession of the subject and if not, proofs have to be rather consistents, except if you’re lucky and make of the whole a political affair, where proofs are less important. Very often it is enough to accuse someone of homosexuality, antisemitism or related in order to obtain a negative judgement for the same while proofs are lacking.
4. If you choose the subjective path, you’ll need some objective proofs, at the end, too. A subjective path means that you are lead by an impression that leads you to situations and facts that finish by relating themselves to the criminal. It is actually much more effective than the objective path, but has no legal consistancy. The fact is though that the knowledge of the crime related to ‘alfa’, makes ‘alfa’ usually commit many mistakes and this leads to factual proofs. Needs some psychology, though.