I remember finding it strange when I was first learning about Chinese, that they really don't have words for yes and no. It seemed obvious that any language would have that. Now I think they're unnecessary words, and what the Chinese do is better.
If you type yes and no into Google Translate and ask for the Chinese equivalents, this is what you see:
But the translation of yes here is more like "is" and the translation of no here is more like "not have".
And this is what's different. The general approach when you're asked a question in Chinese is to repeat back the same verb that was used when the question was asked. So if the question is:
你有什么食物吗？ (Nǐ yǒu shén me shíwù ma?) which means "do you have any food". Instead of saying "yes", the answer is either "have" or "not have".
And if you're asked if you like something, the answer is "like" or "not like".
This is really quite succinct and effective. Yes and No are really quite superfluous words.
I'll write more soon on the best methods for learning. If you want to get a taste for it in the meantime though, my current favorite site is iTalki, and my favorite teacher by far is Amy He. If you decide to try it, click here and it's cheaper for both you and me.