You did not state the purpose of the circuit. Anyway you can try this:
Combine the LDR in series with a fixed-value resistor to make a simple voltage divider which can act like a voltage source that varies with light. This makes the first part of it. Let's call the voltage at the LDR V_Light. Now you have converted the resistance of the LDR into voltage which can be compared to a reference.
Now use a potentiometer to create a programmable voltage reference. You will use this to set the level that will trigger the comparator.Let's call this reference voltage V_Ref.
The point is to have the comparator compare two voltages. And now you have them, V_Light and V_Ref. All you have to do now is to connect V_Ref to the 'reference pin' on the comparator, you can connect it to the 'inverting input', next is to connect V_Light to the 'V_in', or just the 'non-inverting input'.
Going this way, the comparator will output a logic 1 if V_light is greater than V_ref, and a logic 0 if V_light < V_ref, and the other way around if you interchange V_Light and V_Ref (choose according to application). The behavior of the circuit depends on the trigger level you have set with the potentiometer, and the value of the resistor you have put in series with the LDR to form a voltage divider. You set the potentiometer according to the transition level between 'dark' and 'bright', this goes with trial-and-errors untill you get the satisfactory behavior.
The comparator needs a pull-up resistor. Connect the output of the comparator to the positive supply through a 3K resistor. Any close value should do.