Since the 89C2051 doesn't have an analog to digital converter on board you will have to either use an external ADC, or use the internal comparator.
The '2051 doesn't have many pins, and since you don't indicate how many are already allocated, it may be wise to assume that most are already used. This restricts the selection of an ADC to perhaps one with a serial interface. Since you're only measuring battery voltage, which doesn't change rapidly with time, a cheap slow single channel ADC should do the trick. A Texas Instruments TLC0831, or a National ADC08831 are 8 bit 3 wire serial ADCs and are available from RS Components at their trade counter for less than $10 each. There may be others that take your fancy, or may be available near you.
If the voltage measurement doesn't need to be accurate (how accurate ?) you could use the on-board comparator to monitor the voltage. Set the -ve input to a reference voltage, and connect the +ve comparator input to a voltage divider from the battery voltage to ground. The output of the comparator will be available on P3.6. Don't forget to filter the +ve input of the comparator with a capacitor to reduce the incidence of noise. It may also be a good idea to clamp the comparator input so that it doesn't rise above its maximum input voltage. Likewise for the ADC.
When measuring the voltage, whatever method you end up using, make sure that you take several readings, say 16, sum the readings and then average them, to reduce the noise.
In this case it means to restrict the voltage swing of the measured signal to a certain range, usually the limits of the device that the signal is being fed into. It can also mean to change the bias of a signal to a different reference voltage. The clamp can take the form of a diode, zener diode, transient voltage suppressor, gas discharge tube, etc depending on the situation. It's basically a protection device.
I remember seeing this years ago when working on a dishwasher. I was working on the mechanical side of things but I remember the electronics guy mentioning they used something like this to measure temp. Can you give me some more details of how it works?