There are two different ways to create an 'r sound' /r/, and although the tongue placement is quite different between the two, the sound they produce is very similar. An important aspect of the American /r/ is that the tip of the tongue never touches the tooth ridge during this sound!
Method 1 (solid): The back of the tongue is raised so the sides of the tongue touch the back teeth. The center of the back of the tongue is lower and the air travels through this groove to create the sound. The tip of the tongue may point upward, or may be left low.
Method 2 (dashed): The tip of the tongue is raised and curled back behind the tooth ridge while the back of the tongue stays low.
Students should experiment to find the most effective individual method. Also, the /r/ interacts with adjacent sounds, which can result in positions that are a combination of the above methods.