If you need some help getting started and learning how to build an LED night-light circuit, first watch this video for an overview and explanation of how the circuit works.
To wire the circuit, see the diagrams in Figures 1 and 2. Figure 1 shows the connections directly between the leads of the different circuit components. You can use this diagram if you plan to solder the circuit yourself on a protoboard (you will need to decide how to arrange the components). Figure 2 shows the circuit on a breadboard. You can follow this diagram exactly.
How does the circuit work? Remember to watch the video (starting at about 3:25) for an explanation. Figure 3 shows a copy of the schematic. See the Bibliography if you do not know how to read a circuit schematic. The potentiometer and photoresistor are combined to form a voltage divider. The output of the voltage divider turns the MOSFET on and off (therefore turning the LED on and off) depending on the amount of light hitting the photoresistor. The potentiometer allows you to adjust the threshold at which the LED will turn on.
Figure 3. Circuit schematic for the LED night-light.