This is a hugely broad question and I would encourage you to whittle it down to a time in place, or maybe a small sample of places and times.
The short of it is that most people didn't travel outside their local area during their lives so they didn't need ID. You generally lived with the same people your whole life, and you could mutually vouch for each other's identity if needed for some reason. Travelling to another country was something even nobility rarely did until modern times.
People who did travel would usually prove their identity in a number of ways, the most common being carrying or being preceded by a sealed letter of introduction to your future host. The letter would need to be from someone that the person you were seeing also knew and trusted and also knew you. Due to the nature of introductions of this manner your reputation was very important so letters would not be handed out freely. Other examples might include a carefully documented pedigree outlining your noble blood and relations.
Sorry, we don't allow throughout history questions. These tend to produce threads which are collections of trivia, not the in-depth discussions about a particular topic we're looking for. If you have a specific question about a historical event or period or person, please feel free to re-compose your question and submit it again.
In the 19th century, a [French policeman] (http://en.wikipedia.org/wiki/Alphonse_Bertillon) developed the [Bertillon] (http://www.nleomf.org/museum/news/newsletters/online-insider/november-2011/bertillon-system-criminal-identification.html) system, which verified identity by recording the lengths of specific body parts, in order to identify criminals. Although by this point police mugshots were also in use.