Remember the name of the company that sells the product in the commercial. Then go to that company's web site and search their commercial section for title and artist information.
Memorize a few lyrics from the song on the TV commercial. Next, visit a popular Internet search engine. Once there, type in those lyrics along with company's name and hit "search" to find any websites or forums that might have the information.
Try to find the commerical on a video hosting site like You-Tube. More information may be listed in the title that will help you find the artist information.
Post a question on your favorite Internet forum about the song or go to a music message board and ask the members for the information. (See Resources below for links.)