Commercial washing machines are available that replace your normal, full-size washing machine with a portable, hand-crank system. These use little water and no electricity. On the downside, they typically can wash fewer clothes at one time than an electric washing machine, require physical exertion to turn the crank and don't include a rinse cycle. You must rinse your clothes in the sink and wring them dry, or drain the machine, add clean water and run the machine again.
Several natural options can replace soap in your washing machine. Originating from India and Nepal, soap nuts are the shells of the seed of a certain tree. They create a soap-like substance in water and can be used three or four times. To remove grease stains, cover a stain with Borax and warm water and let it sit for 20 minutes to two hours and rinse with cold water. Spray distilled white vinegar onto your clothing before you wash it to remove sweat stains.
Another alternative to the washing machine is the old-fashioned washboard, in which you scrub your clothes clean against a textured board that you've rubbed with a bar of soap. This method requires a fair amount of elbow grease to scrub your clothes clean and wring them dry. Another method is hand-washing, in which you clean your clothing by hand in a sink of hot soapy water, rinse them, wring them out and hang them up to dry.
Instead of bleach, use lemon juice to brighten your clothes. Soak your clothes overnight in a mixture of 1 cup lemon juice and half a bucket of water. Another alternative is to add washing soda to your laundry. Use between 1/4 and 1 cup of washing soda during the wash cycle.