Grammar: Expressing actions in progress (full form)

You may have learned that 在 (zài) and 正在 (zhèngzài) can be used before verbs to express that an action is ongoing or in progress. They are used to create the Mandarin equivalent of present continuous in English. But that pattern is actually a part of a longer, fuller pattern. It's rarely used in its full form, but bits and pieces of it are frequently used in everyday speech, so it's important to know the full form, even if you don't use it regularly yourself.

Structure 
subject+正在+verb+着+object+呢

It's important to remember that virtually every part of the above pattern is optional, so you're going to see all sorts of variations of it (and rarely the full form). The most common variation is just the "在 + V" pattern that you probably already learned long ago. Another common variation is "正 + V" pattern.

Examples
Some examples using the verb phrase 看报纸:
她 在 看 报纸。Tā zài kàn bào zhǐ 。
她 正在 看 报纸。Tā zhènɡ zài kàn bào zhǐ 。
她 正 看 报纸 呢。Tā zhènɡ kàn bào zhǐ ne 。
她 正 看 着 报纸 呢。Tā zhènɡ kàn zhe bào zhǐ ne 。
All these sentences mean "She is reading the newspaper."