Does reading make us better writers? How?

Yes.

Reading is the foundation of being a competent writer.  

Reading various types of material, widens knowledge, puts passion into imagination and takes the reader to a place you do not have to visit.

To read and to take away one lesson from what has been read is a great achievement for the writer.  For many writers to acheive this fills them with more love for their work.  

Reading allows us to appreciate the different writing styles of writers.  We learn new words, new styles of writing, ways in which we want to write and not write.  

Reading is a powerful tool.  Reading one book could encourage to write a book or material which they would never have tried before.  It's all a learning process.  Reading takes us steps forward to learning about ourselves as writers.  What are willing to write about?  What dare we write about?  How can we improve our writing?  What lessons do I need to learn?  

So reading is an empowering tool and is the writers' best friend.

Always...That is one way how to fulfil vocabulary and shape your writing style...