The Trader unit is unlocked by researching Foreign Trade, and built in cities. Trader units are on a separate map layer, and do not interact with most normal things on a map. They can freely stack with any other units, and they ignore cultural borders.
When a Trader is in a city the player owns, it can begin a Trade Route between that city and another city that is in range, as long as none of your Trade Routes are already going there (for example, if I already have a Trade Route to the city of Athens, I cannot send a second one there), and the player has not reached their maximum number of Trade Routes.
Once made, the Trade Route will last for at least 20 turns on Standard game speed. The Trader unit will move automatically along its path for the duration of the route, but will not finish the route until it has returned to the origin city's tile. When on an active route, the Trader unit will disregard terrain restrictions and move 1 tile every turn, placing a Road as it moves. Don't forget to protect your Trader from Barbarians or hostile civilizations, as it is vulnerable to pillaging.
At the end of the Trade Route's duration, you will have the option of renewing the previous Trade Route, assigning a new Trade Route from the current city, or reassigning the Trader to a new city.