using an LDR, when it sees bright light, the resistance drops to only a few Ohms, when it's dark it's between 100k - 1m or so.
As you increases the light, the resistance will drop across the LDR, so basically you will have a rising/falling voltage across your resistor divider.... now If you take that voltage and place it in series with a cap (not sure the value without getting out the calculator) you can make the Cap slowly rise and fall in voltage - still with me?
The Cap's + terminal goes to a base of a transistor (via a resistor to limit the current further) - then have the LED slowly turn on 
(and slowly fade out as the cap discharges)
I'm curious myself and might go and make it on a bradboard, i'm so bored right now.