Write down the product or company being advertised, and look out for the ad again so that you can listen carefully.
Get a notepad, and keep it with you while you watch TV so you are ready to take down information the next time you see the ad.
Listen for the words of the chorus if there are words to the song. One of the lines in the chorus might be the title, which you can search for.
Examine the company or product’s website, and look in the media or news section. They may have information on their advertising campaigns there.
Call the company’s marketing department. They should be able to either give you the information or put you in contact with someone who can.