How much does it cost? That all depends how fast you want to mine bitcoin. A small rig? Hardly nothing, hell you can mine BTC off your PC but you won't do near as many hashes that if you were to buy a dedicated rig. Then when you do buy a dedicated rig, it'll churn through power like a mofo. Not only that, but it'll be like having a space heater in your room, with the sound of a jet engine.