The easiest approach is to take the value returned from the LDR and feed it into an analogWrite command and use PWM to alter the brightness of the LED. Doing this directly would normally dim the LED as the light was dimmed. The LED was reversed and now operates as the inverse of the value read from the LDR. That is, as the light dims, the LDR returns a lower value, that value is fed into the analogWrite command and as the value drops, the LED gets brighter. Quick, easy, effective.
Here is the code in action:
Here is the board in action:
Happy breadboarding!