Hyrule Warriors amiibo Functionality Detailed
It is now well-known that Hyrule Warriors will be receiving an update to include amiibo functionality, however Nintendo hasn't given many hints about what that may entail. Until now, that is.
As revealed during the Nintendo Direct on November 5th, syncing the Link amiibo up with Hyrule Warriors will give you access to the new Spinner weapon, which appeared as a usable Item in The Legend of Zelda: Twilight Princess.
Tapping any other amiibo into the Wii U while Hyrule Warriors is running will give the player either a weapon that is three star's or lower in strength, a rupee bonus, or a crafting material bonus once per day. Except for Zelda herself--and presumably other characters from the franchise when released--which will give you a weapon of three star quality or higher once per day for tapping in.
At this point, we can only speculate what the Shiek and Toon Link amiibos will do when they launch. It is, however, assumed that they will have more significance than, say, a Mario amiibo would when tapped in.
The first wave of amiibos are coming out on Friday, November 21st along with Super Smash Bros. Wii U and Pokémon Omega Ruby & Alpha Sapphire. Hyrule Warriors will receive an update adding amiibo support sometime in "late November," presumably with the release of the Twilight Princess DLC pack coming on November 27th.