Record a CD of your own music. Columbia isn't going to make any kind of deal with someone they have never heard play, and having recorded music is the only way to get a Columbia executive to hear you.
Develop a press kit that includes all of your relevant shows and any previous recordings you may have done with other record companies (or even an indie label). Basically, this needs to read like a resume of your music experience: where have you played, how long, idea behind your band, what kinds of music do you play and include a recent recording of one of your songs. The press kit is designed to develop interest in you, not get you signed.
Send your press kit to the major agents in your desired genre (rock, R&B, rap). Tell the agent know that you are focused on Columbia. The agent acts as a go between for you and Columbia and is essential to getting your foot in the door. It is rare, if at all, that a Columbia executive will listen to a demo CD and call an artist up on his own. Most of the time this is handled by an agent.
Continue recording and developing your press kit. Columbia looks for extensive experience, a following, and, of course, talent. As the music industry is still about making money, Columbia is not interested in simply promoting every garage band out there. Be professional, have your marketing materials prepared by a designer recommended by your newly hired agent and then work hard at developing relationships within the industry.
Stay consistent at checking back in on your status with Columbia. Have your agent send inquiries every week to ensure that Columbia still knows you are interested. Some of the greatest, most successful artists on the label are there because of persistent hard work, not overwhelming talent.