I've soaked fabric in buckets or in the sink or bathtub or a big kettle or bowl.
I use really hot water and let it soak until the water cools down.
Do you have a drying rack or clothesline or towel bar?
I would put the fabric in a colander until it quit dripping and then hang it on something. Don't hang it by an edge - that might distort the fabric - but hang it so that it "hangs easy"
I agree that a washer and dryer does make the process easier, but where there's a will, there's usually a way.