Whenever we have watched locals do this the result is a snowy white pile of coconut flakes.  We achieved snowy white flakes shot through with brown bits from the husk and lumps.  Nevertheless it tasted great in curry that night.

The next steps are to put the flesh into a tea towel and squeeze out the coconut cream.  Mix the remaining flesh with a small amount of hot water and squeeze again for the coconut milk.

This is a new skill set that we are pleased to have an hope to use extensively in future travels (seriously we do, well Carol does).  We accept of course that in UK we will probably just buy tins of coconut milk and if we want fresh then Waitrose do it in chunks in the chilled counter.