The Russian sound “r” is a real challenge to master not only for those who learn Russian as a foreign language, but also for some native speakers. There are several ways to practise this sound, and my favourite one is through the video below. It is jam-packed with exercises that might seem bizarre at first, but then, when you try it, you will realise that they are extremely effective. I recommend working with this video while no one is watching, because the exercises are quite peculiar for someone who never had to work with a speech therapist before. This video is primarily designed for children and teenagers, however, it is absolutely suitable for adults as well.
This video is prepared by Lidia Monetova, who kindly gave me a permission to translate it and subtitle it for English speakers. Please, choose English subtitles in the right bottom corner.
I think that the first 7 minutes of the video can provide you with enough exercises, but if you want more, go through the whole 20-minute thing. Here, it is better to practise fewer exercises and perfect them until you are really comfortable with the sounds your mouth can produce. You will be surprised by what you can do!