When I first started teaching American English pronunciation, I was focused on all the typical things you were probably taught as well: where do you put your tongue? How wide should your mouth be? Should my teeth touch anything?
The more I've taught pronunciation though, the more I've realized that even with perfect mouth and tongue position, my students were still having some difficulty getting a natural sound.
Then, I learned more about breath.
American English actually shares many vowel sounds with other languages, including /i/ like in "sleep", the /u/ found in "blue", and the /a/ found in "stop". But, ask an American to pronounce these sounds, and you'll hear a big difference!
The reason: Americans are allowing so, so much more air through their throat.
So, this is one of the fundamentals of American accents that not enough people are teaching: try to get more air passing through your throat. You'll be surprised how much of an impact it will have on how you sound when speaking in American English.
Now, it can sound complicated: how exactly do you get more air to pass through your throat? Some techniques you can try right now: try sighing, as if you just came home from a long day at work and you can finally relax. Another technique? Laugh to yourself--not just a light laugh, but really try to feel it down in your stomach like you heard a great joke. As you laugh, you are releasing much, much more air. Once you've done that, you can even try a deep laugh like Santa Claus, who says "Ho Ho Ho" in English.
To get working on other breathing techniques and adding breath to your vowels and consonants, take a look at this video here, which will give you these and more tips you can try to get started!: https://youtu.be/wXW4Wvyrz6g