If you look at a range of runners across different distances you will see as many different styles. There are those who look incredibly uncomfortable and inefficient, but it will still work for them. That being said, there are some guidelines to follow:
Relax. If your arms are too tense and tight to your body you’ll not only be wasting valuable energy but also your movement will be more restricted. Before running, do some arm swings to get the feeling of nice relaxed arms.
Drive forward and backward. This might seem like an obvious one but if your arms are too tense as mentioned above, you may end up rotating from the hips and moving your arms side to side.
Opposite arm and leg. To help with coordination and timing, drive your left arm forward as you stride forward with your right leg and vice versa. Doing this will allow you to maintain a nice rhythm and remember to keep moving them.
Thumb to middle finger. Place (not squeeze) the tip of your thumb on the tip of your middle finger. This forces a nice hand position that will bring you back to being relaxed.