Meditation - how to breathe naturally?

Just starting with meditation, I can't get the breathing right. As soon as I concentrate on breathing (as there is not much else to concentrate on), I **unvolunteraly assume concious control** over when to breath in and out. That leads to either to little or to much breathing and makes me feel dizzy. How ever, when I stop conciously breathing in and out, I don't breath at all - my breathing reflex wont kick in as long as I think about breathing. The result is an awkward cycle of holding breath, turning blue, conciously breathing like just surfaced from a freedive, holding breath again. Not thinking about breathing works only so long before I realise that I avoid to think about breathing... Is this common at all? How do you handle this?