There's also understanding how words, vowel sounds, and sentence flow affects the dialect. English has glottal stops which dramatically affects our words. Like Hanna said, in English (and especially in American pronunciation), rounding of the lips, knowing where the sound originates (either from the mouth or within the throat), is important. There are youtube videos that specifically address the various dialects. If you were interested in the American pronunciation, I could direct you toward those, but unfortunately I don't know about the other accents. However, with the right youtube search, I'm sure you can find some instructional videos where natives breakdown how they sound words, vowel patterns, and consonant patterns. Best of luck!

Besides talking a lot, looking at native speakers' mouths is honestly the best way to understand English pronunciation. I myself noticed a lot of important things just by paying some extra attention to people's lips in videos I've watched. Remember, even tiny things matter - my pronunciation got a lot better when I noticed that native speakers make the L sound a bit differently than I thought. Such a little thing helped me a lot!

Get feedback! What you think you hear and what you think you're saying may not be right. You need someone (ie. a native speaker or an advanced speaker) to tell you whether you sound natural or not. You can use Vocaroo to record yourself for a few seconds, and then post the link on italki for feedback. A few members have already done this.