What you have on your spindle is singles. Congratulations! If you want to keep them that way (and singles are pretty popular these days, so no reason not to!), then wind them from your spindle onto a niddy noddy.
The primary "untwisting" danger is on the several inches of each end. Either (a) don't worry about this or (b) take the last 6 inches and fold it back on itself and let it twist around itself -- that gentle 3" of plied yarn will "hold" the twist at the end while you wind the whole skein around the niddy-noddy. I usually set my spindle on a carpeted floor for this, though you could set it in a shoe box if you don't want it to roll under the sofa.
Once it's on the niddy-noddy, tie a tie around each of the 4 legs of yarn on the niddy. Just a loop, tied around, will do it, or if you want to get fancy, a "figure-8" tie that goes around half then crosses itself and goes around the other half of the same leg.
Then take your skein off the niddy noddy and wash it up! Fill a sink with warm water and some dish liquid or wool wash, then put the skein in for 15 minutes; remove the skein, squeeze out the water, refill the sink with warm water (no soap), put the skein back in for a 10 minute rinse. Remove and squeeze it, repeat the rinse if you feel it needs it. At the end, I roll my skein in a towel and really lean on it, to take out as much water as I can.
Then hang the skein somewhere to finish drying; put a towel or a soup can through the loops at the bottom if you feel it's twisting too much, that will put some tension on it while it dries to keep it from twisting.
And congrats on the spindle-full! way to go!
(posted by me this day on spindlers)