This letter appears to be rather simple, but to refine the sound so that your pronunciation of it comes closer to that of a native English speaker can be difficult. The following are tips on how to achieve a nearly perfect American accent on the letter t.
Our base word is did. I know you are protesting that there is no t in did. Stick with me and you will see how did can lead us to the perfection of t in the middle of a word.
When a native says did, the two d‘s are not the same. The first pushes the tongue out and a little up, while the second pulls it down and in, nearly equally in both directions. Also, the alveolar ridge (the hard bone behind the teeth and the beginning of the roof of the mouth) is touched by the region immediately behind the tip of the tongue, known as the blade. It is a U-shaped area. These are two different d sounds.
Now consider the word butter. We do not pronounce the double-t as t‘s, but as a d sound. However, you have to hit the right d sound or you will be pegged as a foreigner.
This time, the d sound is with the tip of the tongue on the hard palate. However, there is no pushing or pulling. It is a simple tapping with the tip. Do not let any air out of your mouth when you say it. This must be unaspirated.
Now try this sentence: Did the butter taste good? The d at the end of good is like the last d in did not the first d. Many foreigners mistakenly make the sound of the first ‘d’, making it sound more like the German word gut, as in Gutten tag! (Hello!).
Let’s try some more. I will place a 1 by the d-sound that is similar to the first one in did, and a 2 by those that are like the last one. A 3 will represent the d-sound in butter. Remember, d1 you use the blade of the tongue, pushing it out and only a little up. For d2 you pull the blade of the tongue equally back and down. On d3 you tap the tip of the tongue on the aveolar.
Place your tongue carefully and make the movement slowly. Record yourself with your webcam and you will be able to more easily correct your own mistakes by reviewing the recording and trying again.
As you can see, proficiency in English requires refining sounds in your pronunciation at levels that demand focus and intricate care. You can do it, though. It does not require more work than before, only a different kind.