.          Here's a simple problem: "How do you make an LED turn on when it  gets dark?"  You might call it the "nightlight problem," but the same  sort of question comes up in a lot of familiar situations-- emergency  lights, street lights, silly computer keyboard backlights, and the list  goes on. 
Solutions? Lots.  The time-honored tradition is to use a circuit with a 
CdS photoresistor, sometimes called a photocell or LDR, for "light-dependent resistor." (Circuit 
Example 1, 
Example 2.)  Photoresistors are reliable and cost about $1 each, but 
are going away  because they contain cadmium, a toxic heavy metal whose use is  increasingly regulated.  There are many other solutions as well.  Look 
here for some op-amp based photodetector circuits with LED output, and check out some of the 
tricks  used in well-designed solar garden lights, which include gems like  using the solar cell itself as the sensor.  (Our own solar circuit  collection is 
here.) 
In this article we show how to build a very simple-- perhaps even the  simplest-- darkness-activated LED circuit.   To our LED and battery we  add just three components, which cost less than thirty cents altogether  (and much less if you buy in bulk).  You can build it in less than five  minutes or less (much less with practice). 
What can you do with such an inexpensive light-controlled LED circuit?  Almost anything really.  But, one fun application is to make 
LED throwies  that turn themselves off in the daytime to save power.  Throwies  normally can last up to two weeks.   Adding a light-level switch like  this can significantly extend their lifetime.  
Here are our components: On top: a CR2032 lithium coin cell (3 V).  On  the bottom (L-R): the LED, an LTR-4206E phototransistor, a 2N3904  transistor, and a 1 k resistor.   This LED is red, 
blindingly bright at 60 candela, in a 10 mm package.  It 
casts a visible beam,  visible for about twenty feet in a well-lit room.   We got the LEDs and  batteries on eBay, and the other parts are from Digi-Key, but Mouser  has them as well.  As we mentioned, the last three cost about $0.30 all  together, and much less in bulk.    
The LTR-4206E is a phototransistor in a 3mm black package.  The  black package blocks visible light, so it is only sensitive to infrared  light-- it sees sunlight and incandescent lights, but not fluorescent or  (most) discharge lamps-- it really will come on 
at night.   
Our starting point is the simplest LED circuit: that of the LED  throwie, which has an LED driven directly from a 3V lithium coin cell.  (Funny looking example 
here.)   From this, we add on the phototransistor, which senses the presence of  light, and we use its output to control the transistor, which turns the  LED on.   
The circuit diagram looks like this; please ignore the messy handwriting.  ;) 
When light falls on the phototransistor, it begins to conduct up to  about 1.5 mA, which pulls down the voltage at the lower side of the  resistor by 1.5 V, turning off the transistor, which turns  off the LED.   When it's dark, the transistor is able to conduct about 15 mA through  the LED.  So, the circuit uses only about 1/10 as much current while the  LED is off.  One thing to note about this circuit:  We're using a red  LED.  That's because the voltage drop across the transistor allows less  than the full 3 V across the LED.  The full three volts is really only  marginal for driving blue LEDs anyway, so two-point-something really  doesn't cut it.  (Might be able to work around that with a cheap FET--  haven't tried yet.) 
And now, let's build it.  You can certainly put this together 
on a breadboard, but there's something more satisfying about the compact and deployable build that we walk through here.
 
First get the transistor and the resistor.  The 
pins of the 2N3904  are called (left-to-right) Emitter, Base, Collector, when viewing it  from the front such that you can read the writing.  We're going to  solder the resistor between the leads of the Base and Collector of the  transistor.  Unusual part:  hold the resistor with its leads at 90  degrees to those of the transistor while you solder.    
Stay safe when you do this: Use 
Mr. Hands. 
After soldering, clip off the excess resistor lead that is  attached to the transistor base (middle pin), as well as the excess  length of the collector 
 
Next, we add the phototransistor.  Note that it has a flatted side, much like an LED does.  This pin on that side is the 
collector  of the phototransistor.  Solder the collector (flatted side) to the  middle pin (the base) of the transistor, again at 90 degrees.  The other  pin of the phototransistor, the 
emitter, is left unconnected for the moment.  (
Here is an alternate view of what that should look like when you're done.)  
Finally, we need to add the LED.  To do so, we need to know which side  is the "positive," or anode side of the device. Regrettably markings of LEDs are not consistent, so the best way to be  sure is to test it with the lithium coin cell-- put the LED across the  terminals of the cell and, when it lights up, note which side is  touching the (+) terminal. (Usually, it's the one with the longer lead.)   Solder the "positive" lead of the LED to the emitter pin of the  transistor-- it's the one on the left, which doesn't have anything  soldered to it. Trim away the excess lead of the LED that goes past the  solder joint.     Solder the other pin of the LED (the "negative" pin,  or cathode) to the emitter of the phototransistor, the pin on the  non-flatted side, which does not have anything connected to it yet. 

By this point, there are only two pins sticking down below the  components: One that goes to the resistor and collector (rightmost pin)  of the transistor, and one that goes to the emitter of the  phototransistor and to the cathode of the LED. 
To test the circuit, squeeze the coin cell between these two terminals,  positive side goes to the lead touching the resistor.  You can't see the  LED on here because these photos were taken with incandescent  lighting-- it wouldn't turn on. 
Bending the leads to contact the lithium cell a little more  reliably, you can try it out a little more easily. In the photo on the  right, I cupped my hand over the circuit-- so the LED turned on. 
To make this into an actual "throwie," you still need to add some  tape and a magnet, but that's quite easily done.  This one makes a  pretty good nightlight attached to the top of a doorframe-- when the  room lights are off, it shines a bright, bright spot on the ceiling. 
Where to go from here?  While this little circuit can do something on  its own, it would probably also be happy as part of a larger circuit.   At a minimum, note that if you work with batteries that have lower  internal resistance than the lithium coin cells, you should place an  appropriate resistor in series with the battery before trying to operate  this circuit-- or else you may put too much current through the LED.     Certainly, this is one of the easiest and least expensive ways to  control an LED with a photosensor.  (Unlike, say,  
this method?)   You could also consider crossing it with some more extreme mods, like the 
Talkie Throwies that know Morse code, or for more extreme hackers, 
bagel throwies.