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What to learn: Study Advertising or Marketing in college and maybe put emphasis on a digital advertising/marketing program if possible. Check out schools that offer excellent communications or business colleges before you apply. To make yourself most competitive in the Creative advertising field, most people go to Creative Portfolio school (like Creative Circus, Miami Ad, etc) to further learn the ways of the industry and to develop your skills.
Design of the commercials is called the "Creative" side of advertising. Creatives initially come up with 5-20 ideas for ways the advertising campaign can come together, often across multiple media platforms, not just TV commercials. Now that we are in an evolving world of digital and traditional advertising, an idea for a TV commercial has to translate into multiple aspects like billboard (Out Of Home--OOH), which websites to run on, how a banner ad or video can develop, how the ad can be interactive and fun.
Another area to consider is Advertising Strategy. In this role, you work with a lot of Microsoft Excel, numbers and databases to research which media outlets and channels would be good resources for the brand or product you are working to advertise. You also get to be a part of the creative process and sit in the rooms where the "Big Ideas" are presented for consideration as actual ideas for advertising campaigns.
Things to check out for examples of great ads are resources like the Cannes Lions Advertising Festival website (http://www.canneslions.com). The Cannes Lions are a creative advertising festival held every year in Cannes, France. They are pretty much the Oscars for advertising. Other great resources are Advertising Age (http://adage.com) and Ad Week (http://www.adweek.com).
Hope this helps!