My first piece of advice is not to get too hung up on trying to sound like a native speaker. Would you start learning the piano in an attempt to sound like Mozart? The first rule of speaking English is to learn to speak clearly and concisely and remember you won't just be speaking to native speakers: There are roughly 380 million native speakers out there, but as many as a billion people speak English as a second language, you do the math.
Try to avoid using idioms and slang (I always say learn it, but don't use it). It might sound clever to say "You're barking up the wrong tree," but if you use it in the wrong situation, or if the other person simply doesn't understand you, you'll only look silly when you try to explain what you meant to say, or what it actually means.
There's also a saying in English "Have you swallowed a dictionary?" It is applicable to anyone who uses long, complicated words when a shorter word will do. Short sentences are just as good (if not better) than long rambling explanations. The value in what you have to say is what you say, not how clever you look or sound when you say it. So it's a good idea to try to use simple, clear vocabulary, KISS - keep it short and simple