V着【zhe】

着 on the first of two verbs makes that verb the background: the manner of the main action, or the state someone is in while doing it. The main verb comes last and carries the sentence.

Aspect goes on the main verb

了 belongs to the main verb or to the end of the sentence. The 着 verb takes no 了 and no 过.

• × 他笑了说 → 他笑着说
• × 她拿着了一本书进来 → 她拿着一本书进来了

Interrupted in the middle

正 + verb + 着 in the first clause gives an action in progress, and the second clause says what broke into it: "I was eating when the phone rang".

A verb doubled with 着, 走着走着, is a related pattern with its own point.

Picking someone out

V着 + object + 的 + noun identifies someone by a state: what they're wearing, holding or doing.

On its own as an instruction, a verb of holding or listening + 着 says to keep that state: 拿着 "hold this", 听着 "listen".