Washing the fleece is generally the 3rd step of the process, after shearing and skirting. A lot of alpaca can be spun without washing with no problem at all. It depends heavily on the animal, the owner, and the shearer.
I skirt my fleeces while I shear, then again when I wash. Go through by the handful and pick out any hay, straw, burrs, grain, second cuts, crud, and mung in general (VM to the spinning world).
I really like to use these big mesh bags. If you stuff it too full it won't wash correctly, but I've found if you lay the fleece one layer thick through the bag, it will wash well and stay together. Using a bag helps preserve your locks, and keep fiber from going down your drain. It also helps prevent felting as you can lift the whole thing at once and hang to dry, you don't have to pull out bits and squeeze the water out.
The bag is very lightly packed, with one layer of fiber. When you start packing the bag fuller, it doesn't wash well and you have to wash it again. After you've washed the same fiber 2-3 times you realize washing less at a time really is the faster way to go.
Fill the sink with hot water and add enough Dawn to tint the water. With alpaca the water temperature doesn't matter as much, but warm to hot is best. With wool you need as hot as possible, and with heavy-grease wool you often need to add some boiling water to the hottest water your tap puts out.
But for alpaca, warm works fine. If I'm dealing with a really dirty fleece, I'll put it in hot water with Dawn, and let it sit for 2-3 hours or overnight. That way all the dirt has dissolved and dropped out. Without waiting for this you'll be tempted to agitate a little to get rid of the dirt, and on fine fleeces you'll end up with a lot of felting. This also usually gets rid of more dirt/sweat and eliminates one of the rinses.
After it's soaked long enough to make you happy, pull the bag out and let it drain. Most the time I'll dunk it back in once and pull it out again. Dunking it in and out slowly will remove dirt, but not cause felting.
Drain the sink and refill with hot water.
I usually lay the fiber out on a towel and roll the towel up to squish out the excess water. This helps prevent felting over just pushing it down on the towel.
Then lay it all out to dry. This is a full fleece drying it front of an open window. Now sing and dance because it's done! :)