My advice:
1)Practice tuning by ear. And tune using as many different tuning styles as you can come up with, but not with a tuner. Try to match it up with a recording for reference. Over time, this should help develop your ear to help notice discrepancies in pitches. We start off hearing music as contour as kids, and over time we learn to hear pitches more finely, and the idea of learning by ear is basically just a further refining of this hearing.
2) Learn as many songs as you can that have accurate/semi-accurate tabs. You'll start understanding how certain paterns relate to certain sounds, how certain intervals feel, and you can visualize it with tab, so it helps a lot. Start with accurate tabs (from store bought books), and after a while, you will begin to notice that some tabs on the internet just don't sound right. It's mostly a matter of training, like anything else you want to do in life. Stick with it and it should come to you in time.