Apart from the obvious, I think people should learn grammar structure. Grammar patterns are not so difficult and if used enough can be internalized. It was a long time before I found out that Chinese not only has SVO sentences but also expository and topic/comment sentence structures.

My approach to learning Chinese has always been an emphasis mainly on just two things: developing a good accent and pronunciation, to include proper tones and tonal inflections, and studying grammar. If you are good at these things, people generally will think you are good at the language regardless of your vocabulary and reading abilities.