New ropes are always fun. I've always tried to uncoil them with my arms through the loops and unwinding it, but it always ends up a mess. Today I got smart though. What you need for this: a 2x4 2 feet long, one 5-6" bolt (any size but mine was 5/16), two big gutter nails or landscape spikes, hammer, measuring tape, a drill, drill bits, and a fence post or side of your woody.
Mark the center of your 2x4, then drill a hole slightly bigger than your bolt. Measure the inside coils of your rope, and place one gutter nail at half that distance from the center of the board to one end (I predrilled the nail holes with a slightly smaller size than the nail to keep from splitting the wood). Place your coiled rope over the nail, pull it tight along the length of the board, and place your other nail. Bend both nails out slightly. Find somewhere you can drill a hole the same size as your bolt to hold the contraption vertically, and drill it 1-2" feel. Put the contraption up, and start unwinding.
I had to hold the loops on the nails for the first bit, but after that it sailed off onto my rope bag.
Brilliant! I've always tried to do the 2 arm twist uncoil. Make it about 1/2-3/4 of the way through and then get tangled and give up. First time out a rappel will straighten any thing needed out, but I like your solution.