The two notes in each group there are meant to be played at the same time. You could finger pick it, using your thumb and index finger, use hybrid picking, which means you pick the lower notes with the pick and the higher ones with your middle finger, or strum it, using a fret hand finger thats not busy to mute the string in between the ones that are supposed to be sounded.
And God said, 'Let there be rock!'
-And it was good