Market state -> price forecast
Price forecast + other factors (risk, liquidity) -> trading decision
If you know (or have a good guess) how the algorithm works, you can work out what state of the market would lead to a price forecast in your favour, i.e. would lead to the algorithm offering liquidity at a price favourable to you.
You then manipulate the state of the market to look like that (generally this is "spoofing" or "layering"), wait for the algorithm to respond, and then take advantage of the favourable liquidity it offers.
When people calibrate their algorithms, they use real market data. Most of the time, someone isn't actively manipulating the market, so the model is not calibrated to handle those situations.
I know someone who used to work at an algorithm trading firm and did electronic market making. He said they used to go to great lengths to program their algorithms to try to spot this sort of manipulation, but it's a hard problem because you're fighting against a cloud of bad traders who are coordinating their efforts across multiple market centers.
I have to say, the regulatory dept. at the exchange I work for does an excellent job of monitoring for any funny business. They have some nifty real-time tools that are scriptable and can replay the state of the market at any point. It's really cool stuff!
You then manipulate the state of the market to look like that (generally this is "spoofing" or "layering"), wait for the algorithm to respond, and then take advantage of the favourable liquidity it offers.
When people calibrate their algorithms, they use real market data. Most of the time, someone isn't actively manipulating the market, so the model is not calibrated to handle those situations.