The first thing that you need to do is to select a band that you fancy. You will have a variety of options to choose from, such as a boy-band, girl-band, male solo, female solo and even co-ed bands. Pick the band that interests you. There is no rule against liking a particular kind of band or music, so feel free to pick more than one band if you want, though it can take you a bit longer to get acquainted with the Korean music if you pick more than one band.
Once you have picked a band of your interest, start listening to their music. Either get their songs from iTunes and listen to them on your iPod, or simply download them to your computer from the Internet. You can also transfer the songs from the computer to your cell-phone and use air-phones to listen to the songs of your selected band on the go. The more you listen to Korean music, you more you will learn about it.
Try to search for pictures of the band in order to familiarise yourself with its members. It would be best if you are able to find pictures of the band with the name of the members written on it, as this would make it really easy for you to learn who is who. You will also need to learn which band member plays which instrument and who is the lead vocalist.
If you can get access to a Korean music show, it would help you become familiar with the personality and other habits of the group members. You will find yourself finding a particular kind of music if you know the person or group singing it.
Open up the Wikipedia page of the Korean band or singer that you selected in the first step and familiarise yourself even more with the members, while also learning about their beginning, achievements and discography.