Recording piano keyboard. 10 points!?

Hey guys, i have a keyboard the Casio AP-45, underneath it has room for cables and headsets and all and i want to start recording really nice sound for my youtube videos. I have currently just been using the camera sound but i've seen other youtubers who hook their keyboard to their laptop/ desktop and it sounds much better (www.youtube.com/user/thejrpiano if you want to see what it sounds like atm) So what can i purchase to record like that? I am new to all this so if there is also any software i would need, please let me know! Thanks much!