I used to hand wash almost everything when we (just DH and I then) lived in an apartment. I put a plastic tote in the bathtub for big things, and had a 5 gallon pail for smaller things. Water was included in our rent, but the apartment had no laundry hookups, despite being huge- two bedrooms, an office, a sunroom, a dining room, a kitchen with a porch, and 300 sq ft living room with a giant fireplace in it. Thus, I had a lot of space to hang things to dry. The only laundry machines in the building were in the basement, and we were on the top (3rd) floor, no elevator. Plus the machines barely worked and were nasty. Handwashing was less of a pain and WAAAY cheaper.
DH was a chef at a country club, so we had a manual 5 gallon salad spinner on rotating loan. He'd bring it home once a week, I'd use it, he'd take it back to work (relax, he'd run it thru the washer and the sanitizer before it got used for greens). I'd really like to get a wringer, but they cost $100 new and haven't been able to find one used... yet!
I had a broomstick with holes drilled in either end and a length of chain thru the holes. I kept in the linen closet. I installed two plant hooks over the bathtub and in front of the fireplace, and I'd hang the broomstick from them by the chains. This was my laundry drying rod. After I washed and spun my clothes, I'd put them on hangers (sometimes I had to clothespin them onto hangers) and hang them from the broomstick. If it was cold or someone needed a shower right away, I'd hand them in front of the fireplace, but usually I just left them in the shower.
Large linens were trickier. I was still using machines for those when, one day I was leaning waaay out the sunroom window to look at a bird's nest and found an ancient pulley on the side of the building. I showed it to DH, who sanded it and WD40'd it, put it back up, and then talked to the neighbors and got a clothesline hung. It was always fun hanging sheets on that, I felt like an Italian American, turn of the century, New York housewife.
I think that in order for 100% hand washing to be practical, you need:
-Equipment, specifically a water removal device, be it a spinner or a wringer, and some type of agitator, as well as appropriately sized basins.
-A means to dry. An outdoor line is great, but unless you live in SoCal, you probably will need to dry indoors some of the time. ( In our house, with a bunch of kids and a bunch of pets, this is tough to come by. We only really have space in the damp basement, so it can take awhile. I've been trying to figure out a way to put some sort of air dryer over our pellet stove in such a way that the pets/kids cannot swing from it/knock it over.)
-A three person or less household, or a two person or more laundry squad.
I have often thought of using a dehumidifier as part of an air drying regimen, but it freaks me out, because we have never paid more than $100 for a dryer, and a dehumidifier would cost us $150+. Also, since we switched to a front loader and a gas dryer, our utilities have gone way, way down. Despite our water rates being raised a lot, our bill has stayed the same, and we have our gas down to $88/mo, year round (dryer, hot water, range, and boiler heat) and our electric down to $77/mo despite the highest electric rates in the state (we use 350 kWh/mo as a family of five). I am afraid that, because dehumidifiers are hogs and we'd have to have the thing on virtually all the time, it would cost us more than our dryer does- it certainly would cost us more in electricity, and I don't think that would balance the relatively small gas savings, since I line dry outdoors whenever I can.
On the other hand, for an apartment dweller (especially if electricity is included in the rent!) or someone else with no laundry hookups, I can see how a dehumidifier would work very well, since it's just plug 'n play.