Fleecewife may be able to describe in words how to take a bit of raw fleece and spin it between your fingers into yarn - she's done it before.
OK this will help you to understand what happens to fleece when you spin it, as well as being part of how to assess a fleece for spinning
Go to one of your shorn fleeces and remove a lock - like a lock of hair, it's a small bunch of wool, in the order in which it grows so pulled out in one piece. Even just removing this from the fleece will teach you something about how a fleece is held together.
So have a good look at that lock. You will see it has a cut end and a tip; the cut end is called the butt end, and the tip is called - tada - the tip

In Texels, Suffolks and most modern breeds, that lock will be 'blocky' in other words it is about the same width and thickness from butt to tip. In certain primitive breeds which have a double coat, you would see that the lock is triangular in shape, wider at the butt and narrowing to a point at the tip, with softer wool nearer to the body and hairier or coarser wool or hair towards the tip.
Often the tip in particular, but sometimes the butt, are a bit stuck together, so use your fingers to open up the fibres. This allows each fibre to move over its neighbour and not stick to it. A fleece which does this is nice and open, and could be spun directly from the fleece without further preparation. If it won't open up, but is matted together, then you won't be able to prepare the fleece by hand. If it's badly matted then you won't be able to get it machine carded either. In fact, seeing if your fleece is matted or open is the first step in assessing your fleece for spinning.
Once you have opened out your lock, you can either roll it into a soft sausage shape, or you can just fold it over the finger tip of your non-dominant hand. With your dominant hand, take hold of a tiny amount of fleece, either from one end of the sausage (which is called a rolag) or from the middle of the folded lock, which will be on the top of your finger, with each end hanging down. Don't pinch your rolag but let it lie loosely in your hand, like a little bird.
Pull the fleece in your dominant hand away from the rolag, pinching the bit you are pulling as you twist, twisting all the time between your thumb and first or second finger (a rolling motion a bit like snapping your fingers), and keeping pulling gently . Pinching at that point will stop the twist running up into the rolag. If the twist does run up into the rolag you will find it very difficult to pull, or draft, any more. This is one of the characteristics of fibres, where it is far easier to draw from untwisted fibres than from twisted ones, and is something to experiment with.. Experiment with how much you need to twist to make a singles thread. You will find that you are limited by the length of your arms with how long your thread will be. Once it's as long as you can make it and is spun enough to hold itself tight, but not so tight that it twists and turns, loop the middle over an upright bit such as a chair back, or someone's finger, or your big toe, then bring the two ends together, allowing the two ends to ply into a two-ply length of yarn. You can give this an extra twist or two if it's very loose. Initially the yarn would unwind, so make a tiny roll with it.
Keep playing with bits of fleece, finger spinning as described, or just drawing it out to see how wool behaves. You will find that quite magically the wool fibres seem to want to cling to eachother - this is because each fibre has little scales along its length and these hook onto eachother. Other fibres don't have these scales so can need more experience to spin.
You can try combing the lock to see how it's often easier to spin from that. You can also try a different type of spinning - worstead as opposed to woollen, by doing your finger spinning directly from the tip or butt end without making a rolag or fold. You will see that will give you a smoother yarn but you may well need to twist it more.
Try this whole process with your various sheep breeds to see how they compare.
For a full fleece assessment there is plenty more to do, but this is how to finger spin. Once you try spindle spinning or wheel spinning you will be producing longer lengths of yarn then wrapping them onto the spindle to hold the twist.
Phew - a picture certainly would be better than a thousand words