Throttle position, air flow rate, air temperature, engine speed and others are measured and used for calculation. The calculation is quite accurate only if all the sensors are accurately adjusted, so adjustments of these is best left to the experts. The computer operates in open loop mode, ignoring the oxygen sensor when it suspects the sensor is not working. Remember the sensor must be hot to work so after start up the computer is waiting to see the sensor output go high first before it will change to closed loop mode. In this mode the other sensors are still used to make the main calculation, but the result is modified slightly according to the sensor output.
Some computers learn as they go and are able to calculate a more accurate fuel requirement faster.
There are other times also when the oxygen sensor is ignored. When accelerating hard with the throttle beyond about three quarters open, the mixture will be set rich to provide more power. When coasting down from high speed the mixture will go lean. If you install a dash mounted mixture display you can see this happen as you drive. To control your mixture as you drive, it is a simple matter of intercepting the oxygen sensor output before it reaches the computer and offsetting the signal slightly.