Could you specify what time period you're thinking of? It would vary a lot from civilization to civilization, and era.

There were a lot of things that could be used to distinguish people that would not have been easily replicated. Certain insignia like a signet ring, sceptre, or crown. Or official papers bearing the seal of their government, monarch, or whatever. Other times the size of a person's retinue would make it clear that they were a person of note.

Now adays a diplomat presents his credentials to the other country's head of state, who then acknowledges them and accepts that diplomat as an emissary.

Before the invention of the steam ship and the railroad, travel was rather limited and it was mostly the upper classes that did it, bar some special circumstances such as going on the hajj, a pilgrimage or a military campaign or crusade.

An upper class person would travel in style, often with a large following, and people mostly trusted the claim that they were who they said they were.

The upper classes often travelled to their own estates or to allies, relatives or friends, who would be informed beforehand and prepared to recieve them - and be able to vouch for the arriving guests in case anyone thought to challenge them.