You will need a computer equipped with a webcam, microphone, speakers, and reliable internet connection.
You can use your mouse to write on the online whiteboard, but I highly recommend investing in a digital pad with pen.
I personally use a Wacom tablet with pen. My opinion and experience is that it is easier to write with a pen than writing with a mouse. Also, it is more comfortable. Below is a link for the Wacom tablet with pen I use and recommend for my clients. I will be glad to help you set it up in a session if you decide to get one.