I've found that most countries have different ways of saying things in different areas of the country or in nearby countries. As an Australian, I can immediately detect a Kiwi (New Zealander) if they say "fish", as I hear them say "fush" instead. We pronounce "tomato" like "tomarto" but the US folk say it like it's "tomayto". We say "banana" like "banarna" and they say it like "bananna".
And of course the same thing happens in China.
I have friends that describe northerners as using "Pirate Speak" because they add the sound "R" to the end of many words. (Pirates are renowned for saying "Arrrgh".
Most in the southern regions don't do this, so a northerner is easily detected.
Here are a few examples:
Instead of 一点 (Yīdiǎn) which means "a little bit" being pronounced like "ee dee enn", they say 一点儿 (Yīdiǎn er) which sounds like "ee deearr". the "n" sound is gone.
Instead of 一会 (Yī huǐ) which means "a little while" being pronounced like "ee hway", they say 一会儿 (Yīhuǐ'er) which sounds like "ee hwarr".
Next time you hear someone speaking Chinese, see if you can pick the "arr".
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.