Voltage dividers are really simple. You have an input voltage (Vin), a common ground and an output voltage (Vout) you wish to achieve. Stick two resistors (R1 and R2) across the positive and ground rails. The junction where R1 and R2 join will be a voltage somewhere in the middle. This "somewhere" can be determined by the formula:
 
Vout = ( R2 * Vin ) / ( R1 + R2 )
 
Where R1 is the resistor connected to positive, and R2 is the resistor connected to ground (this order is important, otherwise you'll wind up getting the voltage drop on the wrong resistor!). When building a circuit, it is important to remember, we are controlling a ratio, if Vin always remains the same, by playing with the figures of R1 and R2 we control Vout. This will become more evident in the first example. Using some magic voodoo algebra we can rearrange the equation to be more helpful for building circuits (the above equation is great for troubleshooting though!):
 
Vout / Vin = R2 / ( R1 + R2 )
 
A worked example - you have a 9V battery and a lamp which requires 6V to illuminate.
Vin = 9V
Vout = 6V
R1 = ??
R2 = ??
Vout / Vin = R2 / ( R1 + R2 )
6 / 9 = R2 / ( R1 + R2 )
2 / 3 = R2 / (R1 + R2 )
So we know R2 is in a ratio of 2:3 with the sum of R1 and R2. From here, we can work out that R2 needs to be a ration of 2:1 with R1. So, a 2k and 1k resistor should split the voltage nicely.
For more details, refer to Wikipedia's article on voltage dividers, though this will be most of what you'll probably come across for simple DC circuits.