Those spiral branches are indeed really cool.
The fruit goes through color changes from green to yellow to red and eventually brown when it dries out. You can harvest the red fruit (probably even yellow fruit) and leave it in a paper bag, where it can pop without you losing the seed. I like to use fine (nail) scissors and cut at the base of the fruit, avoiding direct contact with any sap that might come out. At some point when it's warm and dry, just put that bag in the sun nearby and you should hear the popcorn going within an hour or two if the fruit is mature.
