It grows in many places round the NZ coast, growing most lushly in spots that offer it some shade. To harvest, pick the growing tips - this encourages new growth. (I.e. Leave some for me! :o)
Update 31 January
Beach spinach is in berry at the moment. I'm not sure exactly how edible or good for you the berries are, but spurred on by my intrepid friend Lynda, I've tried a couple. The taste is mild, salty, sweet and juicy with a texture a bit like watermelon.
Beach spinach is in the same family as iceplant, and that has berries that are known to be edible.
Beach spinach links:
Blog post about beach spinach berries
More blogging about beach spinach
Google Images
Plants for a Future database (It doesn't have an entry on beach spinach, but it does have one on its close relative - NZ spinach)
