Fast travel is available from the world map. On the map, dark markers indicate locations you know about but have not yet visited, while light markers indicate locations you have selected. Select any light marker to travel there.

You cannot fast travel from inside dungeons or interiors, or while in combat, or when enemies are nearby. While fast traveling, time moves forward depending on how far you go. So you could start a trip at morning and get to a town at night. If you have your own horse, it will fast travel with you. If you fast travel to a city, your horse will be placed in the nearest stable. Followers will also fast travel with you. NPCs you are escorting will also usually fast travel with you, depending on the quest.

You can only fast travel to a place you have already been. You can fast travel to many points of interests, not just cities and towns.

If you need to reach a far area (for example since a quest takes you there) and you have not been anywhere near it so fast traveling is not an option, you can hire a horse carriage to take you to a capital near your destination. You do not need to have visited a capital in order to be able to hire a carriage to go there. Carriages are a good solution if your quest marker takes you very far away, and you do not feel like running all the way. Just locate the capital city closest to your destination and hire a carriage to take you there. After the carriage has taken you there once, you can then from that point on fast travel to that capital city since you have discovered it.

You can take a carriage from most capital cities. The first horse carriage you encounter will probably be in Whiterun, which is the capital closest to Riverwood. Hiring a carriage costs certain amount of gold depending on the destination. A Carriage can take you to the following capitals:

Downstar (50g)
Fakjreath (50g)
Markth (20g)
Morthal (50g)
Riften (20g)
Solitude (20g)
Windhelm (20g)
Winterhold (20g)

To hire the carriage, talk to the driver and let him know your destination. Then climb up to the back of the carriage, at which point the gold will be deducted to your inventory and the ride will commence. You can also ask the driver for some lore and information about the current city.