If you want to record sounds into your notebook, you just need to connect the audio out into your notebook's audio in. Best is if you have an audio interface which receives in L and R audio in - then you connect L audio out into L audio in (same for R). If not, then you can still connect the stereo headphone out from the microkorg into the stereo in of your notebook - not recommended (since the stereo in is usually a mic input).
If you want to sequence the microkorg with your PC, you'll need a midi cable and a midi interface. Korg midi out -> midi interface midi in -> USB to notebook; midi interface midi out -> Korg midi in.
Many audio interfaces also has midi in it.
Lastly, you may want to consider software. There are license-free software you can download. Otherwise, consider lower end version of Cubase/Sonar or if you are using a Mac, Garageband. If you are just starting off, don't need anything too expensive and high-powered.