To remove the back/wooden piece all you need is a credit/debit card push the card down between the wood and metal frame and gently lever the wood on one of the long sides upwards moving around the side as you do it bit by bit it will come away, there are no wires attached to the wood.
Once removed you will see the battery, which is stuck down with double sided tape which you gently peel away using the same credit/debit card, the electrical connection just pulls out horizontally, in the video they disconnected the single black wire to give access to the battery multiplug, but I just moved the wire out of the way instead.
All in all the battery took about 2 minutes to replace, then a factory reset was needed, but as the new battery was only charged to 57% I let it charge up to about 85% before doing the reset.
Once reset it seems to be working fine and the black spot is not to be seen, as I assume the original battery was starting to bulge against the LCD screen.
I would also recomend that you earth yourself to avoid any static that coiuld harm the moment components.
Cheers
Derek