I will explain below how to record the audio output from your Privia to your computer.
But from the question, it appears that your goal is to produce a video, with a separate, clean audio track to go with the video.
To do this, you will want to record both the video and audio - (with all the ambient noise and extraneous sounds you want to eliminate), with your video recorder - at the same time you are recording your clean audio from the direct signal being output from the Privia. In order for your video recorder to pick up the audio, you will need to be able to send the sound from keyboard to an external monitor and feed the clean direct audio output to your interface - at the same time.
The reason you do this, is to make it easier to synchronize the clean audio to the video. On any decent video editing program you will be able to import the audio only file saved on your computer and line it up under your video's audio file. By having both audio wave forms on the screen, you can zoom in to any section and match them visually and just drag one to line up precisely with the other. Find a part that has some obvious dynamic peaks. Then you mute the sound from the camera while playing the clean audio file, to be sure it syncs up perfectly with the video. Then you render (mix/finalize) your video with the sound file from the video recorder muted. You end up with a video of your hands playing, and a perfectly synchronized audio that is nice and clean. Having the the audio from the video to visually align with the clean audio wave form will save a ton of wasted trial and error time.
Now for recording the clean audio signal output from your Privia. As tarun mentioned, you should use some type of interface to plug the Privia into and the interface will plug into your computer. The headphone/line out jack on the Privia is where you will plug your cable that will run into your interface. You will be recording the exact audio signal you would hear through the headphones.
The Scarlett 2i2 Scarlett 2i2 Focusrite that tarun uses appears to have exactly what you need to produce a video with clean audio. It allows you to run a signal to a audio monitor (so you and the camera can hear the output of the keyboard) while you record video of your hands while recording one audio track to the video recorder and the second clean audio track to your computer. You will need a DAW (Digital Audio Workstation) program as mentioned by tarun to convert the output into a file your computer will recognize (WAV, Mp3). Many of the audio interface devices come bundled with this type software.
Another way to do what you want to do, and much more, is to use a multi track recording device that does not require DAW software and will save your music to an SD card. I use a Boss BR 800 and I do something very similar with audio and video. Using the BR 800 I can send the signal from my instrument to both a monitor and record it directly through the output jack and a cable, so my video recorder will pick up the sound I am playing on my instrument that will be the same sound that is going directly through a cable from my instrument to the recorder. As mentioned above this will make the synchronization easier.
To learn more about the Boss BR 800 and other interfaces that will allow you to accomplish your goal - read this Record Instrument To Computer
You plug your Privia into an interface or recorder the same way you would plug a guitar into one. Run the appropriate cable (such as a 1/4 inch TRS to 1/4 inch TRS cable) from headphone/line out on Privia, to line in on interface - same as a guitar.
Good luck and have fun!