Yes, they receive payment for routing their order flow to specific market makers. KCG (Knight Capital) and Citadel are the two players that typically get the vast majority of the retail order flow. Two Sigma is starting to get in the business as well. The exact amount Robinhood receives is going to vary considerably, but it primarily depends on if the order takes liquidity(market orders + marketable limit orders) or adds liquidity (normal limit orders).

Retail brokers typically end up making ~$0.001 per share + commission + fees + interest on cash balances + financing spread from margin lending and stock loan

Robinhood makes $0.001 per share + fees + interest on cash balances + financing spread from margin lending

I'm skeptical Robinhood will ever be able to become profitable. They're great for the consumer (except for their heavy marketing of margin lending), but I don't see them attracting the power users they need to make the business model work.

If you do use Robinhood:

1) Build a well diversified portfolio (30+ companies) 2) Don't use leverage 3) Don't trade on a daily/weekly basis