On this page of the Ghost Of Tsushima guide you can find out the rules of fast travel. This is a very helpful mechanic, as Tsushima is rather huge, and reaching the chosen location may take a lot of time, even if on horseback.
Fast travel is available only for all those locations which you've already discovered, and only those where there are no opponents. If, for example, you come across a location occupied by the Mongols, you must first get rid of them and "recapture" the area.
After choosing a location from the world map, just press Triangle button. The important thing is that fast travel is free and does not consume any supplies.
You can fast travel from any location in Tsushima. You don't have to reach a signpost or any other such object.
The game may temporarily block the use of fast travel. There are two main reasons for such a restriction.
The first reason is the presence of opponents in the immediate vicinity. You can't use fast travel if you're under attack or simply if there are enemies in the immediate vicinity. You must kill all the surrounding opponents or escape them effectively (i.e. end the chase).
You can't fast travel during some of the quests. The game will not allow you to activate fast travel, e.g. if you are traversing a map with a companion, or moving around a closed location associated with one of the main objectives of the mission. You have to complete the entire task, or at least the actual part of it.