wait until the seeds are orange and feel soft, not hard. Pull and scrape off all the orange stuff until you get to the hard seed inside. It's hard to do, so your fingernails will hate you for a day or so. Soak the seeds in warm water for 3 days, changing the water daily. After that dry the seeds outside for a few hours and sterilize them with alcohol. Put them into a baggie full of moist (not wet) and sterilized sphagnum moss and perlite and put the baggie somewhere like your water heater where it'll get warm but not hot. It may take up to 6 month, but you should get a good germination rate. Pot these up when you see roots forming.

Well, they've been soaking in daily changed water now for 3 days, and yesterday I noticed these long green things emerging from the part where they were connected to the branch. Hmmmmm Are these roots or leaves? Dilemma!

If they come out of one of the 3 "eyes" near where they connected to the tree, they are leaves and ready to plant. If they come from somewhere else, they might be roots (I think they are leaves though) and they are also ready to plant. Congrats on your new queen palms!