You have to form a voltage divider and take your reading from the centre (the * in the above drawing). Without two resistors (the LDR is just a special type of resistor) you are just pulling the Arduino pin low and so will always read a value of 0.
Now if for some reason you live in outer mongolia and can't get a resistor and just want to play to see what happens there are two ways to do this.
1) If you have a second LDR use that instead of the fixed resistor, as you light and shade either of the LDRs the reading will change.
2) Use the internal pullup resistor instead of the external resistor (I'm pretty sure this will work with an analogue input).
Both these methods will be very imprecise but will at least allow you to have a play.
Personally I'd just go and get a resistor.