Smashbros.com has a whole page about amiibos. It mentions how the amiibos join the battle, how they level up, their personalities, abilities, and much more.

Here's some pics from the website!

Figure Players Join the Battle 

Adding figure players to the game is easy. When selecting fighters to play in a Smash battle mode, simply touch the NFC touchpoint with your amiibo and a figure player will appear in an empty fighter slot.

Abilities

Feed equipment you pick up in the game to your figure players to raise their attack, defense and speed. You can also give a figure player up to three abilities by feeding it equipment with special attributes, and you can customize your FP's special moves as you do with other fighters in Custom mode.

Personalities

Figure players will pick up tactics from strong opponents. There is no maximum level for this—FPs will always be willing to learn from superior fighters!

Presents 

Figure players will obtain custom parts and gold during their battles--they’ll then give these gifts to you after the fighting is done.

Link: http://www.smashbros.com/us/howto/entry8.html

The UI looks really nice and I'm certainly excited to try these out. Things like "explosive perfect shields" will certainly make my practice more interesting.

You should probably put in the text explaining what each picture does cause its a bit confusing otherwise

It is pretty neat though

Lol, they got Bowser Jr. in there.

Done. Thanks for the feedback!

not sold on their functionality. I'll buy them for collection purposes

and jigglypuff XD