How can one know if an isnaad in a hadith is valid?

To determine if a chain is valid is largely an intellectual exercise requiring research. One of the basic requirements for a hadith to be sahih (authentic) is it cannot be a mursal, munqati' or mu'dal hadith. The mursal is what the tabi’een (narrator in the generation after a companion) has narrated about the Prophet (saw) without mentioning the companion. The munqati' hadith is one where a single narrator is missing in one or more places in the isnad. The mu'dal hadith has two or more narrators missing consecutively from one or more places in the isnad. All of these lack continuous isnads which take them out of the sahih category. If a continuous chain exists, the next step is to look up the biography of each individual in encylopaedias known as Ilm al-Rijal, which are famous compilations of what is known of all narrators. An example would be Taqrib at-Tahdhib by Ibn Hajar (Ilm al-Rijal) by the Shafi'i scholar and muhadith Ibn Hajar al-Asqalani. These usually give biographies of narrators including where they lived, their dates of birth and death, family members, where they travelled, who they studied with, whether they had a sharp memory or not, level of piety and studies, and whether they were regarded as upright or not. It is possible then to undertake a number of tests to determine if the chain is likely to be authentic or not, such as the narrators who allegedly heard information from another narrator actually living in the same era and region or did travel to the other's city and met. Likewise if the a hadith is transmitted from a teacher to a student or family member to their descendants and so on. Through such verification tests it can give us the confidence the chain is accurate or not.