A car sputtering at idle could be caused by a number of different things such as clogged or dirty fuel injectors, low fuel pressure, bad fuel pump, water in fuel, bad airflow sensor or bad or dirty oxygen sensor.
A faulty engine computer or even a bad coolant temp sensor could be causing engine sputtering at idle.
It's hard to actually tell unless I were there to look at it but it would be a good idea to have a mechanic look it over if you're unsure on how to fix the problem.
I would recommend trying some fuel injector cleaner poured into the gas tank to see if that helps clear it up and also add some Heat fuel system cleaner which gets rid of the water in the fuel.
Another thing to do is find the coolant temp sensor and check to make sure the connection is fully secure and not loose.
The last thing I would check too is the Throttle Position Sensor because it could be stuck or not operating properly and may not be letting the computer where the throttle is position at which messes with the engines computer.