The above functional block diagram shows generally how a monostable multivibrator (MMV, or one-shot) works. Not all of them have every part shown, but this is the most common internal block diagram.
Basically, the external resistor (R) and capacitor (C) determine the output pulse length (tw) of the device. This value can be directly calculated from the equation:
tw = k*R*C
k is a constant that is determined from the datasheet, directly linked to the size of capacitor used and the operating supply voltage of the device.
There are three ways to trigger an output pulse:
(1) A falling edge at the A\ input while CLR\ and B are both held HIGH
(2) A rising edge at the B input while A\ is held LOW and CLR\ is held HIGH
(3) A rising edge at the CLR\ input while A\ is held LOW and B is held HIGH
When any of those 3 events occurs, the nFET connected from Rext/Cext to Cext is activated and the capacitor is discharged very quickly. At the same time, the output (Q) is switched HIGH (Q\ = LOW). A comparator monitors the discharge of the capacitor, and when it reaches the appropriate level, the nFET is then turned off and the capacitor is allowed to naturally charge from Vcc and R. A comparator monitors the voltage on the capacitor for when it reaches 63.2% of Vcc (which takes one time constant, ~R*C), and then the output switches off. In some devices there is a pFET also connected to Rext/Cext (as shown in the functional block diagram above) to force the capacitor voltage quickly back to Vcc to reset for the next cycle.
There are two types of MMVs
(1) Retriggerable - These can be triggered while the output is active and it will extend the pulse length. The output will turn off one pulse width time from the last trigger.
(2) Non-retriggerable - These cannot be triggered again while the output is active. The pulse will terminate one pulse width time from the initial trigger regardless of any additional triggers