How do prop trading firms and prop traders make money?

In a standard brokerage trading setup, a trader uses their own funds to place trades, and the firm would derive its income on a commission or percentage basis from acting as a broker on behalf of its clients. 

In the case of prop trading, the firm is using its own funds, so it earns 100% of any profits or losses that it makes on trades placed in the market.  Props traders earn an agreed share of any profits that they make in their own portfolio of trades.