Disclaimer! I am an Arduino newbie. I just did 'Hello World' last night. Proceed with caution!
To control the lights based on time of day I think you'll need some sort of real time clock. Perhaps you can use something like one of these:http://www.ebay.com/sch/i.html?_nkw=arduino+rtc
I also found this which looks like you can get time of day without adding RTC hardware:http://playground.arduino.cc/Code/time
I suggest that you look for projects that people have done that are similar to what you are trying to do. This may be helpful:http://www.instructables.com/id/Arduino-controlled-window-for-cat/
I like Jeremy Blum's Arduino tutorials. Very newbie friendly.http://www.youtube.com/user/sciguy14/videos?view=0