American speakers pronounce R by making the tongue tense. When the tongue is tense, the throat naturally becomes a little bit tight. Make sure that the tip of the tongue does not touch the top of the mouth.
In grade schools, American teachers compare the R to a growling sound made by a cat. If you think of that, it could help you to tense the tongue and throat in the right way.
You can also think of the consonant Y sound as in yes. With this sound, we tense the tongue just a bit. R is made in about the same way except the tongue is much tenser.
If you are not used to this R sound, you just need practice. Remember: Americans pronounce all R sounds–whether R is first, middle or last.
Use the video to listen and repeat common words.
Air, Area, Care, Carry, Chair, There, Their, Where.