Same Way One Filled Wash Tubs
Either via hose from a faucet, or fetching containers of water back and forth until you had enough. In the case of "cold water flats" and or other homes without plumbed hot water supply, you had no choice but to boil water by the kettle or whatever full until there was enough to get the wash done. Again same as using wash tubs, including the fact you could keep reusing the same "hot" wash water until it became "warm", then "cool".
By the time "modern" wringer and other washing machines were becoming common enough appliances, home planning changed to accomodate in that normally kitchens or laundry areas had room around sinks to manouver washers close to the source of water and drains.
Many older homes had those huge and or low/wide "laundry sinks", with high taps. These are great for not only doing laundry, but for filling large containers (such as buckets), with water and easily hauling them out.
Of course well into the era of "modern" washing machines, you still had them located out on back porches and so forth. In those instances see above, that is women (or whomever was doing the washing), carried on as they always had done. The one saving grace is you could simply drain the water into the yard, or use it easily to wash down the porch/steps.