Read classic literature. The books that survive to become classics typically contain sophisticated sentences and a broad vocabulary. Read them without rushing. Absorbing their language will improve yours.
Make sure to learn any word you don't know. If you can, retrieve the meaning from context. If you can't, look it up in a dictionary.
Make a vocabulary list. Write down all the words you miss in a notebook, along with their definitions. Review it every week or so.
Slow down. Be aware of what the person talking to you has said and how you want to respond. Get in the habit of choosing your words. You will be amazed at how much it improves your speech.
Be aware of English shibboleths. Shibboleths are dialect markings indicative of your class. Basically, they are somewhat arbitrary indicators of good English which people will notice and judge you by. For example, if you say "y'all" or "ain't" or use double negatives, many people will judge you to be uneducated. Follow the link below for a guide to some standard shibboleths .
Associate with people who speak good English. Join a debate society or a study group. Not only will you learn eloquent modes of speech but, as the people in your group become your friends, you will unconsciously imitate their speech styles in order to fit in.
Consider hiring an accent reduction coach. The standards of "better" and "worse" are culturally biased and arbitrary. Although such bias is appalling, having a particular dialect might lead others to make unfair assumptions about your sophistication and intelligence. Accent reduction coaches can help you to speak the standard dialect of whatever region you live in.