〜ようだ
it seems, apparently (from evidence); like
Plain form + ようです · Noun + のようです · な-adj + なようです
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Plain form + ようです gives your judgement from what you've noticed: 誰もいないようです, "there doesn't seem to be anyone here" (it's quiet, the lights are off).
Nouns take の (雨のようです) and な-adjectives take な (静かなようです).
It also makes comparisons, "like": まるで夢のようです, "it's just like a dream". まるで ("just like") often signals this use.
Compare the neighbours: そう (looks like) is about appearance, そうだ (I hear) is about what you were told, and らしい leans towards hearsay. ようだ is your own conclusion from the evidence in front of you.
Casually, the same thing is みたい, the next point.
Register: みたい is the casual equivalent.
Examples
電気が消えています。誰もいないようです。
The lights are off. There doesn't seem to be anyone here.
田中さんは風邪を引いたようです。
Mr Tanaka seems to have caught a cold.
外は寒いようですね。
It seems cold outside.
会議はもう終わったようです。
The meeting seems to be over already.
まるで夢のようです。
It's just like a dream.