我的理解是。在，比较口语化。正在，一般用在书面的场合比较多。 比如说你的朋友问你，你在干嘛？what are you doing? 中国人一般不说，你正在干嘛。 而一般的书面的东西比如报纸，杂志，文章里面的句子一般会用正在。比如说，他正在看书。或者，他正在吃饭的时候，电话响了。这种情况也可以理解成，在，只是表示一个状态。而，正在，强调的是更确切的时间，exactly. 着，也是表示状态。这个不知道怎么解释。但是一般会说。我躺着看书。坐着吃饭。坐着看电视。走着上班。跑着去找他。等等。希望对你有帮助。

verb + 着 = doing..., with..., plz attention the comma here. It means that this is not a complete sentence. for example, Walking in the street,I met one of my friend. in Chinese, we call the part, such as "walking in the street", 从句. 从：followed so the part like this is a part, which is following the real sentence. here the real sentence is: i met one of my friend. --- in chinese we call it 主(principal)句. the function of 从句 is to supplement some information for 主句. another example: with time passing, my father becomes old. 从句：with time passing 主句：my father becomes old. verb + 着 is used in 从句. BUT, we don't use the same structure like english. Zack has given us some examples: 我躺着看书。 in this sentence, 主句 is 我看书。 ---- I read a book. 主句 has all basic information.( subject, verb and object). 从句 is 躺着. "躺着" describes the way how I read a book. It supplements a kind of way for this 主句. Attention: sometimes, 主句 could be omitted. for example, you always do anything in bed. One day, your mom says this sentence below to your father: 他总是躺着看书，躺着吃饭，躺着看电视。 It seems that this is a complete sentence BUT it's NOT. here, this is still a 从句. In fact, the whole sentence should be like this: 他总是躺着看书，躺着吃饭，躺着看电视，你能不能教育教育他！ Your mom omitted the 主句：“你能不能教育教育他！” why? because when she talks, she is sure that your father definitely know what she wants to say. Here, 从句 supplements the REASON why "你应该教育他"（主句）. As your father, he definitely know what your mother meant even if your mother just said the 从句。 从句 could be used for 原因、目的、状态 etc. BTW, In chinese grammar, there is NO the definition of 从句 or 主句. It has another way to explain all of this. I used the two words to help you understand "verb + 着".

nice question. 在 + verb = be doing 我在看书。 means exactly I'm reading a book. 正在 + verb = be doing ... right now it emphasizes the fact that you are busy with something RIGHT NOW. e.g: - let's go shopping. - No, I cant. 我正在工作。 here, if you say: no I cant. 我在工作. It's OK, no error. If you want to emphasize that you are busy right now, you should use 我正在工作.

一般都会说我在看书，其实表达的意思就是我正在看书。 我们不会说我看着书.

I forgot one thing: 正在 + verb + 着 means someone is doing something and keeps the state. e.g. 我们正在学着如何做饭。 vs 我们正在学如何做饭。 If we translate them in english, it seems that they are the same: We are learning how to cook. But in chinese they are a little different. 正在学着 emphasizes that the action which is acting is our state for now. What is our state for now? -------- learning something. For most of cases, the difference could be ignored.