Picking, in fiber prep terms, is a word usually associated with a big and dangerous machine. It has spikes that pull apart fiber into little fluffy shreds to open up dense fibers and allow debris to fall out. Picked fiber is usually carded next, but it can also be spun directly for an uneven textured yarn. But you don't have to have an expensive machine to do this, the first pickers were fingers and these are still an effective tool. They are also far less likely to accidentally shred your clothes in the process.
Some people call the hand process teasing, but to me this sounds too gentle. You really do want to rip the fleece apart as much as possible. But to avoid breaking the actual fibers, it needs to be done a tiny bit at a time. Fingers are great for this, because the person connected to them can nearly automatically compensate for a stubborn lump or pull out a bit of Not Fiber. This sounds pretty tedious, some people do it while watching television. I often do it while I'm thinking up new article ideas.
What you need:
To start, divide the fleece into finger-sized sections. It can be raw or scoured, although I always scour. The fine fleeces I prefer get pretty greasy and I often have to leave them sitting around for months or years before I get to them. More grease means hard and crunchy wool after it dries out — scouring is not a complete solution but much improves the situation. Also, dry bits of junk fall out more easily from a clean fleece because there is less for it to stick to. Drape the cloth on your lap to catch the debris.
Hold the staple whatever way is comfortable for you and start pulling it apart a little at a time:
The motion should be quick and steady, as you work you will have a staple of fleece in one hand and a pile of fluff in the other. Don't worry about pulling fibers completely away with each pass, just grab a few and yank. Stuff those loose fibers in your palm and do it again.
As you go, pull out things that shouldn't be in there: bits of leaf, sticks, clumps of dirt, matted tangles or very short bits of fiber. Don't break stubborn fibers but stop and pull them apart more carefully or declare it a tangle and get rid of it.
Put the handful of fluff aside and keep going. Stop to rest your fingers and move the finished fiber to your big container every few minutes. Don't underestimate getting it safely out of the way quickly, this avoids picking up the loose junk you just spend all that time getting out. Try not to squish it down too much in the container, the more open it is, the easier it is to work with later. (If you cram it all back into the original bag, you will have to fluff it up again later.) If there is a lot to do in one sitting, get up and empty your lap cloth once in a while.
Now your fiber is ready for carding. Opening the fiber first reduces the number of times you need to card to get a uniform batt. That can be a big deal if, like me, your usual drum carder is on the other side of the city in somebody else's basement. You can also spin the picked fiber by the handful for a yarn with bits of crimpy wool sticking out.