Discussion of Amiibos goes here. Any questions or tips on the inner workings, strategies, or uses of Amiibos can and will be put here. The thread will be updated from time to time, to provide the most up-to-date information.
So far, confirmed working Amiibos for Fire Emblem Fates are
Ike (Vanguard)
Lucina (Great Lord)
Robin (Tactician)
Marth (Lodestar)
The upcoming Roy Amiibo is unconfirmed so far, but likely compatible.
The Corrin Amiibo, currently in development, is unconfirmed so far but not so likely, due to the gender neutrality of the character. But who knows? They let Robin in.
Only Fire Emblem character Amiibos are compatible with Fire Emblem Fates. (Sorry Shulk fans)
Characters gained from completion of the Amiibo-accessible Hero Battles cannot gain support levels with any characters, Amiibo or not. They can still use the Pair Up option, but no support is gained.
Hero Battles are unlocked after scanning Amiibo figures three times, but you must complete a battle in between each before scanning again.
On the first two scans, the Amiibo character will give you one of its respective accessories, then go to work at either the Armory or the Accessory Shop.
Upon the third scan, the character will challenge you to a battle. A map location called "(Amiibo's name) Hero Battle" will be unlocked until you challenge the location. If you lose, you will have to rescan to challenge them again.
Upon completion of the Hero Battle, you will gain a unit based on the Amiibo character.
From each scan onward, they will be sent to work at either the Armory or the Accessory Shop, where you can purchase either their Mock Weapon or Accessory, respectively.
Each Amiibo character fights with their signature weapon.
Ike uses Ragnell and has a proficiency in swords and axes.
Lucina uses Falchion from FE:A and has a proficiency in swords.
Robin uses Levin Sword Thoron and has a proficiency in swords and tomes/scrolls.
Marth uses the Falchion from FE:SD and has a proficiency in swords.
If and when Roy is compatible with Fates, he will use the Sword of Seals.
EDIT: There was already a thread about this stuff. It's somewhere in the comments, if you'd rather go there. I was dumb, didn't realize it existed until it was brought to my attention.