This could be a number of things:
Incorrect fuelling due to a faulty water temp sensor. If this is the problem then the ECU will be leaving the car constantly ' on choke' and not reducing the fuelling as the engine
warms - so unplug the sensor and clean the contacts on both sides with some switch / electrical cleaner ( not WD40) and inspect the wiring for any signs of damage to the insulation especially where it runs over other components and through the bulkhead- if this doesn't help consider replacing the sensor as they're not expensive
Check for exhaust
leaks before the O2 sensor as if this has been experiencing an exhaust leak then it will have been running very rich as the sensor will see the extra air pulled in as fresh / lean fuelling and be adding fuel to compensate.
this can lead to catalyst failure as the extra fuel can re-light inside and melt the catalyst
The best way to find an exhaust leak is to run the engine from cold and feel around the exhaust joints with your bare hands - you'll have about 30 seconds before it all gets too hot and you should feel any escaping gas blowing over your fingers
Air leak at the mass airflow meter -
Any air dragged after the meter isn't 'seen' by the ECU and so not compensated for, causing rough running.
Check the hose clips for tightness and inspect the trunking for any cracks or splits and also all the vacuum system, the small bore pipes and fittings for cracks and missing parts.
The best way to locate a leak is to have the engine running and warm and then spray lighter gas around each joint in turn. If the engine rev's up you've found your leak.
Check that all the wheels can be turned freely by hand, and free off any sticking calipers
Incorrect wheel alignment:
Check all the tyres for signs of uneven wear if it has any then get it checked out at a place that does 4 wheel alignment not just front tracking and ensure tyres are pumped up to their recommended maximum
Injectors are clean and not dribbling - add a bottle of injector cleaner to the tank
Use good quality fuel - from my own findings its worth paying the extra for BP or shell as typically you'll get another 10% fuel saving which outweighs the cost over supermarket fuel.
And the biggest thing is driving style, by not labouring the engine ( too high a gear up hills etc) and not accelerating hard away from the lights etc you can usually improve things by another 25-30% or so.