My grandmother was a spinner, weaver, knitter, crocheter etc. Her house was full of woollen items.
I wash large woollen items in the bath tub as others have mentioned. I usually use a mild shampoo (wool is hair). I use warm water and add the shampoo to it before the woollen item. To help get the water through, I use a clean toilet plunger gently.
I drain and rinse several times (until the water is clear), leaving the item in the tub the whole time.
I do not line the tub with a sheet as it just traps the dirt and I want it to drain away. After the final rinse I let it drain for quite a while, pressing it until no more water came out. Now I roll it out of the tub onto a sheet and carry it outside. I have several old sliding door screens that I put on saw horses for drying.
I do not worry about drying in sunlight. The sheep lived outside before they were shorn.
I have washed rugs, curtains (yes my grandmother made them out of wool), very old crochet afghans and more this way.