If you want to become a better copywriter, read aloud what you have written. So often I read a block of copy and am pained by the lack of thoughtful sentence construction. I'm writing this after reading an ad that had three you's and one yours in a single 10-word sentence. It was one of those sentences you re-read just to try and give it the benefit of the doubt.
Just as an art director must pick his fonts and design every element in each ad, so too should a writer. Writing is a craft and as a copywriter you should know the art of the English language, starting with the basics.
Learn these terms and what they mean: alliteration, meter, consonance, cadence, and onomatopoeia. They teach you about the sounds and timing of words and syllables that make copy easier on the ear. Learn what they mean and apply them where appropriate. Pick your words and 'design' how they sound and feel. Then say your copy aloud. If it sounds funny, it probably reads funny too.