The Nintendo Switch comes with two controllers, called Joy-Cons. Here’s a demo of how they work.
When you play the Switch on the TV, you’ll set them in the Joy-Con grip, but they can be removed to play with friends and can each be used as a fully functioning controller. They have an NFC Reader/Writer for Amiibos support, and also have a capture button for capturing and sharing screenshots form gameplay. The right Joy-Con has a motion IR camera the can track the shape and motion of objects in front of it.
The Switch will either come with black Joy-Con or red and blue Joy-Con. Extra controllers will cost $50 for either the left or right controller, and $80 for a set of two.