To Make Something Clear
To Clear Something, To Strain
transitive verb, godan verb
澄む is "to become clear" - this is when you make something clear, because you must (ます) make it clear. You have to. That's why this is or to make something clear or to clear something.
This can also mean to strain when used together with 耳, as in 耳を澄ます, "to strain one's ears".
すます
The reading is the same as the kanji, so if you know that, that'll make this answer clear too.
今立て込んでるんだ。後で戻ってきてから泥水を澄ますよ。
I'm in the middle of something. I'll come back later and make the muddy water clear.
私は、一つ上の階からコンスタントに聞こえてくる気味の悪い金切り声を聞くために、耳を澄ましました。
I strained my ears to hear the faint but constant screeching coming from upstairs.
少佐は、大佐に怒られても澄ました顔をしていた。
The Major kept a composed face even when the Colonel was angry with him.