clock - How to generate edge-triggered pulse

First, a bit of background: I am just a hobbyist with electronics and have very little formal education in the area. I understand most terminology, but generally require a schematic for me to be able to create something of any decent complexity.

I am working on a personal project in which I have run into a bit of an issue. I have a digital square wave that I need to transform into pulses. My guess is that there is something that can output a pulse on the rising edge, but I don't know what it would be called. Sorry if this has been asked a thousand times, or is something elementary. I've tried searching all over and am not sure what something like this would be called. I want a circuit to transform a digital waveform that looks like this

____------____------_____

into one that looks like this

____|_________|__________

using common ICs and/or passive components that a hobbyist might have around.

Thanks.

edited to remove superfluous details

Edit:

Maybe I can rephrase the issue in another way, instead of shortening a pulse to some undefined short duration. What I want is to divide a clock by 4096, such that every 4096 pulses, I can get a pulse of the same duration as the input clock.

i.e.

_-_-_-_ ... x4090 ... _-_-_-_-_

becomes

___________________________-___

Answer

To make a pulse generator, use a resistor, a capacitor, an AND gate and an inverter:

^{simulate this circuit – Schematic created using CircuitLab}

To make a dual-edge-triggered pulse generator, use a resistor, a capacitor, and an XOR gate:

^{simulate this circuit}

EDIT by another user: An excellent answer with one caveat: As the signal into the gate is now analogue best use a Schmitt version for the 2nd gate. These are available in NAND and NOT versions but less available for AND or XOR. It will work with non Schmitt versions but there may be a few power spikes on the rail and/or non full logic values at the 2nd gate output.