Today Nintendo announced that each Amiibo figure will cost $13, and that the first wave of Amiibos will release in 2014. This first wave includes: Mario, Donkey Kong, Villager, Peach, Yoshi, Link, Samus, Pikachu, Fox, Kirby, Wii Fit Trainer and Marth.
As of right now it's unknown which characters will be in the second wave, and also when these Amiibos will come out. Nintendo have said they'll release more information on the functionality of Amiibos soon.
In the meantime, you can already pre-order characters from the first wave of Amiibos if the concept interests you.