Easiest way to understand 着?
As a native Chinese speaker, I would think twice if I see &quot;着&quot; in ancient Chinese or in genteel writings. It is a hard character to learn. But the most common usage in modern Chinese, especially casual and oral occasions, is &quot;function word&quot;(虚词). It gives a hint of the mood and tense of the sentence but does not have a concrete meaning.
To make things clear, I would quote Modern Chinese Dictionary(《现代汉语词典》)'s full explanation but give my own comments to each meaning.

着【zhāo】
1 （～儿）（名）下棋时下一子或走一步叫一着：高～儿｜支～儿。
2 同“招”。
3 〈方〉（动）放；搁进去：～点儿盐。
4 〈方〉（动）用于应答，表示同意：这话～哇！｜～，咱们就这么办！

Comments: None of these meanings are common.
The first two are noun uses. Both are gradually substituted by &quot;招&quot; -- whether in chess play or not. A strict editor may correct you and use &quot;招&quot;. The only case is in the proverb “一着不慎，满盘皆输”, only the original &quot;着&quot; is correct.
3 &amp; 4 are northern dialect, around Beijing I believe. Very very rare. I've only heard this expression in TV series about BJ life in the last century. I can't think of any other cases.

着【zháo】
（动）
1 接触；挨上：上不着天，下不着地。
2 感受；受到：～风｜～凉。
3 燃烧，也指灯发光（跟“灭”相对）：炉子～得很旺｜天黑了，路灯都～了。
4 用在动词后，表示已经达到目的或有了结果：睡～了｜打～了｜猜～了。
5 〈口〉入睡：一上床就睡～了。

This is the most confusing pronunciation I believe. The neutral tone &quot;·zhe&quot; is the most common one and this is the second most.
There are some fixed combinations: “着调”(1)、“着凉”(2)、“着魔”(2)、“着迷”(2)、“睡着”（4&amp;5）、“点着”（related to fire, 4). In these cases, you are almost certain it is &quot;zhao2&quot; not &quot;·zhe&quot;.
Also when it's &quot;verb+不+着&quot; or &quot;verb+得+着&quot;, it must be &quot;zhao2&quot; not &quot;·zhe&quot;.
For 1, it is used as an active verb, not a functional verb, so it is not following a real verb. It means “挨着”、“够着”, &quot;reaching&quot;. But it is also a very rare usage.

着【·zhe】
1 （助）表示动作的持续：他打～红旗在前面走｜他们正谈～话呢。
2 （助）表示状态的持续：大门畅～｜茶几上放～一瓶花。
3 （助）用在动词或表示程度的形容词后面，加强命令或嘱咐的语气：你听～｜步子大～点儿｜快～点儿写｜手可要轻～点儿
4 加在某些词后面，构成介词：顺～｜沿～｜朝～｜照～｜为～

This is the most common usage in Modern Chinese. When you see “着” following a verb and not with a “不”(or &quot;得&quot;), most likely it is a neutral tone &quot;zhe&quot;.
However, this usage does not exist in ancient Chinese / classical Chinese （文言文）.

着1【zhuó】
1 穿（衣）：穿～｜吃～不尽。
2 接触；挨上：附～｜～陆｜不～边际。
3 使接触别的事物；使附着在别的物体上：～笔｜～眼｜～手｜～色｜～墨｜不～痕迹。
4 着落：寻找无～。
着2【zhuó】
1 (动)派遣：～人前来领取。
2 公文用语，表示命令的口气：～即施行。

This part is very confusing for Chinese pupils as well. There are many fixed combinations under this usage as well.
For &quot;着2&quot;, it is most often in &quot;着人&quot;, meaning &quot;sending someone&quot;, but a more polished way than “派人”. Not your first choice of writing or speaking but you might see it in some places.
For &quot;着1&quot;, I would suggest you just remember the following words: “着笔”、“着力”、“着陆”、“着墨”、“着色”、“着实”、“着手”、“着眼”、“着重”；“沉着”、“附着”、“胶着”、“衣着”、“执着”
Yes, there are more words to remember... so if you see a &quot;着+noun&quot; pattern, &quot;zhuó&quot; is more likely than &quot;zháo&quot;. Also, people are using both pronunciations interchangeably in many words. Here I listed are the ones I believe not quite proper for the other pronunciation.
For &quot;verb+着&quot;, here are the very few fixed combinations you can only use &quot;zhuo2&quot;. If it is after a word meaning &quot;stick&quot;, use &quot;zhuo2&quot;
Notes:
&quot;执着&quot; can be written interchangeably with &quot;执著&quot;
&quot;穿着&quot; can be &quot;chuan1 zhuo2&quot; or &quot;chuan2 ·zhe&quot;. &quot;chuan1 zhuo2&quot; is a noun, or an intransitive verb, e.g. 他的穿着(n.)很时髦；他穿着(v.)入时.  &quot;chuan1 zhe&quot; is a transitive verb, e.g. 他穿着时髦的衣服。

This answer is getting super long.
So my ultimate rules are as following:
&quot;verb + 着&quot; is most likely &quot;·zhe&quot;, especially when it is used as a transitive verb. Remember some of the &quot;zhuó&quot; combinations, and when it's about clothing or sticking.
&quot;verb + 不 + 着&quot; and &quot;verb + 得 + 着&quot; are &quot;zháo&quot;. &quot;睡着&quot; is always &quot;zháo&quot;. &quot;Reaching&quot; is always &quot;zháo&quot;.
&quot;着 + noun&quot; is most likely &quot;zhuó&quot;. But remember the &quot;zháo&quot; combinations. The line between &quot;zhuó&quot; and &quot;zháo&quot; in this form is a bit vaguer.

I hope this long answer can be somehow helpful. I'm a native Chinese speaker, but inexperienced in explaining Chinese in English LOL. Let me know if anything confusing.