This is a dead simple way to accomplish the task. There are of course other ways to wash fiber and wool can even be spun from the "grease" with no washing at all... but that's pretty nasty. Some animals are cleaner than others and some also tend to just be naturally kind of clean overall but they all smell and even if your unwashed fleece is tolerable when received, it's going to smell when it hits the water.
That said, other than being stinky it's a pretty easy job and requires almost no "tools". As mentioned above, there are several ways to do this. There is even a great Instructable that shows how to wash "dog fur" in a far more modern way that is identical to methods for washing wool.
I learned to process wool in a living history setting for demonstration purposes and have done it countless times. We couldn't use mesh bags or washing machines. Definitely labor intensive but if you only process and spin just a little at a time it's fine. So, that's what I'm showing here.
An important note may be that if you ask around long enough you might be able to get fleece or other fibers "for the asking" but it will almost certainly not be washed. If you are spinning or knitting on a budget this comes in handy. There is also a certain degree of satisfaction in taking wool "from sheep to shawl".
Step 1: What you will need
Wool or other animal fiber(Own a long haired dog?)
A towel or table cloth
Enough very hot water to fill the bucket a few times
An airy place to work and dry your fiber without having it trampled, tracked or blown across the yard
A muslin bag or a large basket
For this Instructable I used a couple ounces of very nice wool from New Zealand that I picked up on Ebay. Raw fleece is substantially cheaper than yarn or even processed wool and is readily available all over the web.
For my bucket I used a simple plastic hardware store model. It could be about any sort of bucket as long as it's clean. Maybe avoid a rusty one but that's about it.
This is incredibly important. You must use detergent as opposed to soap. There is a big difference for this application. Detergent will loosen and float away the oil and dirt and generally icky stuff. Soap on the other hand will not do nearly as good a job at that and will also leave a sticky residue that can ruin your fleece for all but felting. Dawn dish detergent is my weapon of choice. The yellow kind was my favorite but blue is fine too. You can use any detergent you like. Historically this would have likely been something like stale urine or ox gall. Even living history programs balk at this.
A towel or table cloth to first blot the fibers a little and then give them something clean to dry on. I just spread this batch out on the bathroom floor.
Hot water, very hot. You need the water to be hot enough to soften and dissolve the lanolin and other sticky oils. You won't be scrubbing or agitating the fiber so you need the combination of very hot water and detergent to do the heavy lifting for you. It will take several "rinses" with the hot water and detergent to get your fleece clean. So if you don't want to turn up your water heater a bit you may need to heat some water on the stove. Be prepared to heat water while your fiber is soaking in the previous bath. You don't want it to cool off or get cold. That's very bad too.
Room to work is important. It's nice if you can do this on a warm summer day out on the lawn but if you live in a city or are processing fiber in wet or cold weather it's not practical. Just make sure to have enough room to slosh around dirty water and then lay out your fleece to dry where it gets enough air to do so. If your fleece stays wet too long and mildews you'll be sad.
Optionally you could use a loosely woven muslin bag or a large basket that will allow for air circulation. You can hang the bag from a tree or clothes line to dry or leave a basket of fleece in the sun. You will need to gently fluff the fiber to ensure it gets dry all the way through. This option might be important if you have little indoor space or it's too windy to let it dry outside in the open.
A note about the smell, this stuff can really stink up a small space and literally drive family members and roommates outside. It'll serve you well to consider who might have to put up with it before you start.