Yes, there is a correct way of writing Chinese characters.  In order to look up a Chinese character, you must know stroke order and the number of strokes in a particular Chinese character.  To give an example, let’s look at the Chinese character below that means:  everlasting or eternal.   It takes 5 strokes to write this character!

This character shows the correct order as well is the correct stroke order.  So the correct order is always top to bottom, and left to right.  This character also shows all the strokes of Chinese calligraphy.

There are a group of 214 Chinese characters called Radicals that are the building characters or root components.

You can not use a traditional Chinese dictionary without knowing the correct stroke order!

Here is a page below from one of my many Chinese books.