1Of objects, surfaces, or clothing — to get dirty, soiled, or stained by physical substances like mud, oil, food spills, or dust. The everyday physical sense and by far the most common use. Intransitive (the thing itself gets dirty); the matching transitive is 汚す (よごす). The same kanji read as けがれる carries a heavier religious/ritual sense of becoming impure.
雨で靴がすっかり汚れてしまった。
My shoes got completely dirty in the rain.
テーブルがしょうゆで汚れているから、拭いておくね。
The table's got soy sauce on it, so I'll wipe it down.
子供が外で遊んで帰ってくると、服がすぐ汚れる。
When the kids come home from playing outside, their clothes get dirty in no time.
油で手が汚れたので、石鹸でしっかり洗った。
My hands got greasy, so I washed them well with soap.
白いシャツは一度着ただけでも襟が汚れる。
Even wearing a white shirt just once gets the collar dirty.
2Of abstract things like reputation, name, or the heart — to become tarnished, sullied, or morally compromised. Used figuratively for social or moral 'dirtiness', as in 名誉が汚れる (one's honor is tarnished) or 心が汚れる (one's heart becomes corrupted). For the heavier spiritual/ritual sense, the same kanji is read けがれる instead.
スキャンダルで会社の名前が汚れてしまった。
The scandal tarnished the company's name.
お金のために友達を裏切るような人は、心が汚れている。
Someone who would betray a friend for money has a corrupted heart.
不正に手を染めて、彼のこれまでの経歴は汚れた。
By getting involved in wrongdoing, his whole career so far was sullied.