In Chinese people's daily life. There are three most common styles of writing: Kaishu(regular script, I call it standard style), Xingshu( semi-cursive script, I call it running style), and Caoshu （Cursive script, I call it as dancing style). Kaishu is the most common one among the three of them. It is used in the books, dictionaries, magazines, newspapers, and also in the computer and Internet. While most people prefer to write in Xingshu to speed up the writing. In my experience, most doctors like to write their prescription in Caoshu, which is fascinating and very hard to recognize, to keep their prescription as secret from the patients. People also like to sign their name in Xingshu or Caoshu. Some of them write their name according to the calligraphy rules, so it is not difficult to figure out what character they've written. But some of them just invent their own style, then it becomes their special signature. ;-)
My father used to be a teacher in the elementary school. He told me that he started to teach me some characters when I was 3 years old. And I could recognize dozens of characters before I was 5 years old.(Actually I can't remember that ;-) ) My clear memory about learning Chinese is when I was in the primary school I liked practicing writing the same character again and again until I could remember how to write it accurately and quickly. Maybe I started to learn to write in Xingshu style when I was in the Junior high school, I am not very sure about that. And I started to learn Caoshu, the dancing style, when I had the calligraphy class in college. Most of time I write in Xingshu. As for Kaishu and Caoshu, they only happen when I practice calligraphy.
I made this video to show you how to write the character 福 fú in the three different styles I mentioned above.