1In the form ～ようだ / ～ように見える, expresses a conjecture or impression based on what one observes — 'it seems (that)...', 'it looks like...'. Usually written in kana.
彼は疲れているようだ。
He seems tired.
外は雨が降っているようだ。
It looks like it's raining outside.
どうやら道を間違えたようだ。
It seems we took the wrong road.
2In the form ～ように, indicates purpose ('so that...', 'in order to...') or manner ('in the way that...'); common in instructions and wishes.
忘れないようにメモしておこう。
Let me make a note so I won't forget.
みんなに聞こえるように大きな声で話した。
I spoke loudly so that everyone could hear.
先生が言ったように書いてください。
Please write it the way the teacher said.
3Attached after a noun to indicate the form, style, or type of something (e.g. このような 'this kind/style of', 同じような 'a similar kind of').
このような形のグラスは珍しい。
A glass shaped like this is rare.
妹と同じような色の服を買ってしまった。
I ended up buying clothes in a similar color to my sister's.
4After a noun, in the form ～のような / ～のように, expresses likeness or comparison ('like', 'similar to'), including figurative comparison (まるで〜のようだ 'just like...').
彼は子どものように無邪気に笑った。
He laughed innocently like a child.
氷のように冷たい手をしていた。
Her hands were cold as ice.
今日のことは、まるで夢のようだ。
What happened today is just like a dream.
5Used to refer vaguely to a thing or matter 'like that' without stating it precisely (e.g. そんなようなこと 'something like that').
誰かにだまされた、そんなような話だった。
It was a story about getting deceived by someone — something like that.
「明日は休む」とか、そんなような事を言っていた。
He said something like 'I'll take tomorrow off', or words to that effect.