Picking
The first step of processing down a raw fleece is to "pick" it. When doing this by hand, I'd suggest using a picker. The aim is to remove most of the dirt and vegetable matter (VM) from the fleece.
When picking you'll notice the actual color of the fleece changing, lightening due to the loss of dust, but also from the "opening up" of tightily closed locks. In my experience, white fleeces will stay light, but darker colors will regain their deep colors once spun.
Scouring
Scouring is the removal of lanolin from the fleece. You can spin "in the grease" (with lanolin still present in the fiber) but I believe it's less popular, and certainly not recommended for spinning wheels (it leaves residue all over and inside the orifice.)
This step is when it's most likely your fiber will felt, so take care!
Combing or Carding
Now you'll brush out the fiber so all the different fibers will be oriented more or less in the same direction. Broadly speaking there are two methods to do this, carding (which is a woolen style of prep) and combing (a worsted style).
"Woolen" prep and spinning produces a yarn that is warm and soft and has more squish to it. It also is less able to stand up for abrasion.
Conversely, "worsted" prep and spinning produces a yarn that's more sleek and tight and might be less squishy, but is better able to stand up to wear and tear. For example, this is the style I use for knitting socks.
Spinning
And now spinning! There are three basic styles of spinning: supported, drop, and wheel.
Everyone will have their preference, and each style will come with their own set of pros and cons. For example, you'll get more done on a spinning wheel in an hour, but you'll get more done on a drop spindle in a week. And you may think that you need to be sitting to use a supported spindle, but I've actually seen people tuck the bent handle of a ladle into their belt and balance their supported spindle in the spoon's head!
Plying
Everyone will have their preference, and each style will come with their own set of pros and cons. For example, you'll get more done on a spinning wheel in an hour, but you'll get more done on a drop spindle in a week. And you may think that you need to be sitting to use a supported spindle, but I've actually seen people tuck the bent handle of a ladle into their belt and balance their supported spindle in the spoon's head!
Finishing
Last, but not least, is the actual finishing of the yarn. This step serves many purposes, such as evening out the twist, or gently shocking the fibers to add strength to them. Technically optional, but best-practice really is to include finishing your yarn.