All you need is one handboard! If you plan to use it in a condition where you can easily touch the sand with your feet to give a strong push when you get the wave, you can avoid wearing bodysurfing fins, otherwise they are strongly recommended.
You need to get the wave on the crest:
you start paddling with the wave behind you
when it is abut to reach you, you give the last push with the hand where you are not wearing the handboard and you keep the hand with the handboard in front of you
you start putting weight on the handboard without making it sink
at this point you should start gaining speed from the wave and you can start putting more weight on the handboard
enjoy the wave making turns and tricks exploiting the control and the speed obtained from the handboard!
Yes, it depends on the type of feeling you want to experience on the wave. Fins increase stability and allow you to feel like you are on a "rail". The more the number of fins, the more the "rail feeling" increases
Yes, all what you need is being able to swim and to learn which is the right time to get a wave. Make sure to know the basic "rules of the sea" and don't expose yourself to conditions you are not prepared for.