The Japanese R sound is called an "alveolar tap" meaning the tongue quickly "taps" and then pulls away from the "alveolar" ridge behind the top front teeth. The position of your tongue is similar to when you make a D sound, but the tongue moves faster and more towards the back of the mouth on release.
If you're an English speaker, you can find the sound by saying a word like "butter" or "water" quickly over and over without enunciating, so it sounds more like "budda" or "wodda". The consonant sound in the middle should be the らりるれろ consonant.
