How can I sound like a native speaker?

Good question! How can you tell when you're speaking to a non-native speaker of English? (Depending on the characteristics they mention, I lay out my answer.)
Get to know the grammar of the language well. This is the backbone of the language and ensures that people understand you. I will then show two examples: a correct and an incorrect way of speaking, and ask them to discern which is the best. I will then explain that exposure through reading and audio visual tools is the best way to familiarise oneself with the language. A second way is learning idiomatic phrases. These are colloquial ways of speaking that really identify you with a native. I will provide examples. The English equivalent of this is "a car that takes your fancy." Familiarise yourself with different styles of writing: informal, formal, descriptive. These give you a range of speaking. We will practice examples.