It's pretty easy to do. Bitcoin already contains an alternate network with a different genesis block and different network parameters (the minimum difficulty is lower to make generating easier).
Competing with Bitcoin will be almost impossible, however. You'd have to offer something really good.
It'll probably go down like this: Circa 2014. I'll trade my 50 BTC for 0.214 of your OBX (Oprah Bux) -- which is just enough for the iPhone 6 my girlfriend wants.
[Edit: Changed currency name and added code OBX.]