These audio files will help you when practicing tremolo. This is important because, on a mandolin, you communicate emotion with tremolo.
Start by plucking your open "G" string, in time to the music. Use all down picks when you start. After eight beats, switch to eighth notes, but alternate your down picks with up picks. This means you will play twice as many notes, but your right hand will move at the same speed. Do this for eight beats, and then play twice as fast again.
Try to maintain an even sound when you do this. You may find that it is easier to get a more precise rhythm, if you loosen your grip on the pick.
If you are comfortable with that, then try a variation which demonstrates the volume control on your instrument. Do the exercise as above, and start with your pick fairly loose in your hands. This should lead a quiet tremolo when you get to the sixteenth notes. When you are well in to the tremolo, slowly begin to press the pick between your finger and your thumb. The tremolo will get louder and louder and also becomes more difficult to play evenly. This audio file goes on for longer than the previous ones do.