If you have a bad oxygen censor what kind of things will start to happen to a car? Because My car is broke down and in the beginning my car would act like it didn't want to stay started then when I would come to a stop it would shake really bad. then grey smoke started to appear from the muffler? any ideas

Even a bad oxygen sensor couldn't keep the car from starting. It has probably lost spark or fuel to the engine. Listen for the fuel pump "whir" for 2 seconds with the key in on position, not start. Or have the fuel pressure checked, and scan for possible trouble codes. That is the place to start: scan, fuel pressure, check for spark.

Sounds like you might need a valve job.

The check engine light needs to be addressed. Yes it could be a sensor but you need to know.
The light blinking means the problem is serious, such as a dead miss on one or more cylinders. The light being on means something is happening with the engine performance that could damage the catalytic converter.
Get the computer scanned - most auto parts stores will do it for free in hopes of selling you some parts. Once you have the codes research them online or here.

I did that job once on my car, then the same thing happened.. you most like'lly installed it wrong.. pull it apart and see if pieces broke off it... what kind of car is it ?

Fuel pressure regulator can do this. Also bad fuel pump could. Is it getting good pressure out tailpipe? Maybe plugged catylitic converter?

G'day mate well lets start with the O2 (oxygen )censor , it is in the exhaust and does clog up give a spiked reading ( on a graph or multimeter ) instead of a smooth transition like a wave flowing,this will tell all the other censors that the fuel flow/mixture/quality is bad , the rest try to compensate by raising the mixture changing timming etc, get the O2 censor done 1st then go from there, it should calm down once this is done,

could be the coolant temperature sensor.

when a oxygen sensor is bad it shows and acts as if there is problem somewhere in the car. even though you had the O2 censor changed there is still a chance that when they ordered and installed it that it was defected. yeah its stupid but that was what i was told by a mechanic. but thats what that sounds like or maybe transmission.

you know. i took it to a mechanic and actually.... The timing belt cut the Crank Shaft Censor... So it was the crank shaft censor again. The wires were routed wrong from the first mechanic that "fixed" the car.