Hi,
You can break your problem into several smaller ones and solve it one by one.
First, you can try control relay first by using Arduino. This
link might interest you. It has example circuit for controlling 12V relay. I suggest you should be also familar with how relay works. There are plenty of websites or videos online which you can search for, keyword 'how relay works'.
After that you can try integrate 12V light bulb to the relay system. If you know how relay works, definitely you will know how to light up the bulb using that.
Have fun exploring.