Screen Casting on a Raspberry Pi
There are several ways to screencast on a Raspberry Pi. One way is to install screencasting software, such as Istanbul, but this saves as a .ogg file which is hard to convert to a format recognised by YouTube or other popular video sharing websites. The easiest way by far is to access the raspberry Pi by vnc on the :0 desktop. The :0 desktop is the desktop viewed on the local monitor connected to your Pi.
The best way to do this is to install x11vnc on your Raspberry Pi. Do this by running "sudo apt-get install x11vnc". To start up the server, launch the x desktop (if not in already) with "startx", then run (in LX Terminal) "x11vnc -desktop :0". A lot of code will run down the screen, ignore it. Now log into the vnc server from another computer on your network (using software such as Chicken of the VNC), using your Raspberry Pi's IP address and port 5900. Now you can control the desktop shown on the Raspberry Pi's monitor.
Now to record the screen, if you are using Windows then install Fraps or Bandicam, if using Mac then use Quicktime Player. Now you can record your Raspberry Pi's desktop easily and in a YouTube native form. If your Raspberry Pi is in another room, I would recommend using an audio recording device, such as voice memos on an iOS device. If you have any questions, tweet me at @andrepocalypse and I shall do my best.