I looked up how to clean a fleece-some sites were more helpful than others-the two best ones I found are at the bottom of this post.
Here is my pictorial version of how to clean a fleece. It was an enjoyable process-I felt quite rural sitting on my back steps, picking twigs, grass and other less pleasant substances from around the edge of the fleece. This part is called skirting.
Use old pillowcases as you might not want to use them again after this.
When you have done your final rinse, it is advised that you hang up the cases to drain. Then you can, if you have the patience, get handfuls of wool and spin them in a salad spinner. I don't have the patience, so instead I held them up to drain most of the water, then very gently rolled and squeezed them to get more water out.