This was posted last year and I mentioned in the comments that I'd post it again this year.
The following question was submitted anonymously using the form on the right.
I know its kind of late to ask being that Chanukah is almost over but I was wondering, what are we supposed to be thinking when the candles are being lit? And even after when you just look at the lights? Also is this a special time to ask to things and is there anything specific we should ask for then?
It's still not to late to get an answer to your question since there's still another night left to Chanukah. I don't know if there's a source for this but I have heard that when the menorah is lit, it is a very special time to daven for anything.
I also heard that one should look into the flames and let the light of the menorah penetrate your soul. Just by looking at the flickering Chanukah lights, you can affect your neshama. You should just let yourself look...stare...at the flames. It can really impact you very strongly. It helps you get rid of the negative effects of things that you should not have looked at but saw. We live in a world where it is so easy to see the wrong things. Even without trying, just by walking down the street or turning your head the wrong way, images get thrown into your face and then they stay there forever.
So when you look into the flames and you watch the fire dancing, let it talk to your neshama - it can help get rid of the tumah, the impurity, that may have penetrated your soul when you saw things you should not have seen.
When you stand in front of the menorah, take a few minutes to daven. Daven for those people who have never seen the beauty behind the Chanukah candles, daven for the people you know who are waiting for yeshuos, who need a miracle to save them. Daven for those who are stuck in the dark and need Hashem to light up their lives with bracha.
It's a special moment that passes by so fast. The menorah is lit, the family gets busy with supper, cleaning or whatever it is. Some people have a custom to stay by the candles for 30 minutes and say certain tefillos-prayers and specific perakim of tehillim. Whether or not this is your custom, you can definitely take the time to remain by the candles for a little bit of extra time so you can daven for something you are waiting for.
Think about the two brachos that are said when the menorah is lit. The first one is that we were commanded to light the menorah and in the second one we thank Hashem for performing miracles bayamim haheim, bazman hazeh, in those days and in our days. Think about the miracles, big and small, that you were lucky to experience in your life. And think about the miracles you wish and hope for...and beg Hashem to make them come true!
May your tefillos at the candles be accepted and may you be able to purify your soul by looking deep into those flames...and may your neshama always feel like a fire - excited and enthusiastic and ready to do all the mitzvos we are so lucky to be blessed with!
I hope this helps!
Also, please can the person who submitted this question comment to let me know that you read this answer and if you still have a question about what I wrote?