Haha, it is difficult even for a native to decipher very cursive or bad handwriting. Basically, when we read, we are only certain about some of the characters and then deduce other characters based on rough shape, context, or other clues.
As for writing, elementary students in low grades are assigned to repeat writing one character for ten or more times in a row. Chinese students are required to write instead of type for most of their tasks, so, after years of writing, people find their accustomed ways to make shortcut. However, most spontaneous writing styles are far from beautiful or even decipherable. In high school, teachers usually make practising handwriting compulsory. The copybook is the most convenient tool for practice. You write on semi transparent paper and emulate standard calligraphy. It's feasible actually. Many students improve quite a lot after several months of practice.
Though my handwriting is not that good, but I believe it is something average in the sense of immaculateness.
My primary school composition. Posted here as a reference of typical style of newbies.