When I work with a student who wants to improve pronunciation, or sound more like an American, I think it's important to explain exactly how to position or move the tongue, the teeth, and the lips and how to use the breath and the voice - the mechanics involved in making a sound. Then I explain that the new way of making a sound or pronouncing a word must be practiced repeatedly until the muscles of the mouth have memory. Achieving muscle memory means not having to consciously think about how to make the sound.
I encourage techniques like listen and repeat, shadowing, reading out loud and recording/listening to yourself.
What has worked for you?