The first mode is called the one-shot, or monostable, because pin 3 (the output) will go high for as long as you want, but only one time. When the timer runs out, the output resets to low and waits for another trigger event to start again, stabilizing in only one state (off). A good example of this concept is a motion sensing light.

First let's look at the circuit schematic below, and then we can decipher what is going on later.

Push SW1 and the LED lights for a short time, then goes off. The time it stays on is found by multiplying the values of R4 and C2 and is expressed in seconds. The time is not exact, and as either value gets very large or very small, the error increases. A potentiometer of a similar magnitude to but in place of R4 will give you better control over the time. In the end, the only way to know the exact time is to actually time it with a clock.

Larger values for R4 and C2 will increase the time the LED stays on. Why? Well let's take a closer look at what is going on. (Now would be a good time to review the function block diagram from the previous step). Before we press SW1, output pin 3 is low and R3 pulls the signal at pin 2 (trigger) high, so the LED is off and stays that way. We press SW1 and it shorts the signal from pin 2 to GND, which triggers the comparator inside. If the voltage at pin 2 is less than 1/3 of the source voltage, the comparator activates the flip-flop which drives output pin 3 high. Since our source is +9V, we only need pin 2 to sense less than +3V, so the 0V at GND is more than enough. So now our LED is lit. Now what?

Capacitor C2 is initially empty before we press SW1 because it is connected to the discharge pin 7, which essentially connects C2 directly to ground internally and drains it. When we press SW1 and the flip-flop is triggered, the internal connection to discharge pin 7 is cut and C2 is allowed to charge through R4. This is where we get our timer. If the container (large C2) is big or the flow we use to fill it is small (large R4), it takes longer to fill C2. When the voltage across C2 reaches 2/3 the source voltage (so +6V here), the second comparator connected to threshold pin 6 is triggered, switching the flip-flop back to the original state, shutting everything off. C2 is again connected internally to discharge pin 7 and drains back to 0V, ready for the next trigger.

At any time between pressing SW1 and C2 reaching 2/3 source voltage, if we press SW2, we short the connection to reset pin 4, which until now has been forced high because of R2. The reset pin does exactly that, effectively switching the flip-flop back to the original state, turning off the LED and draining C2.