Several ways. The most obvious is color. Easter Eggers will come in all sorts of colors, none of them being real, accepted varieties. Ameraucanas will always be sold prefixed with a variety, e.g. a "Wheaten" Ameraucana or a "Blue" Ameraucana.
Ameraucanas will always have a pea comb, slate legs, a beard and ear muffs. and lay blue eggs. Easter Eggers will generally have a pea comb, slate legs, a beard and ear muffs, and lay blue or green eggs. About 20% will lack one or more of these traits.
Ameraucanas are much more expensive than Easter Eggers - Ameraucanas cost $10-$30 for chicks and $50+ for adult pullets or hens, whereas Easter Eggers will be $3-$6 as chicks and $20-$30 for adult pullets or hens.
Ameraucanas will almost always come from breeders whereas Easter Eggers will be found at common feed stores and the like.