I've installed a new kitchen sink and faucet, however the problem is that once I turned the water on I am able to get water to come through the sprayer (both hot and cold) but not through the faucet it's self. Any suggestions??

Is this something I have done wrong ,or could this be a defect in the faucet?

I assume you are talking about the pull out sprayer on about a two foot flex hose. The button on the sprayer could be stuck, try pulling out on the button. I don't think you messed up on anything. Although it is a pain I wouldn't spend too much time on it, take it back and try again.