The R is similar as in English, but there can be a bit of a throat vibration involved. Youtube is a good source for this sound. I think it is unique to German and probably varies by dialect.
And as I understand, it's not a tongue roll like in other languages, though I've used that method before I realized I could use my throat.
At the end of a word such as Mutter, it isn't pronounced at all. It comes out more Moota, an "ah" sound instead of mooter. Mutter doesn't rhyme with computer :D .