I spent three months hand washing dipes when my son was new born ( I took clothes to the laundry mat then) and recently three months handwashing everything.
What I find most useful is to soak soak soak!!!!
If possible find a bucket with a tight lid and let soak over night with enzymes or even just baking soda if washing dipes. For clothes I just soak in cold water or bs and cold water.
I have never had the priveledge of owning a washboard but have used large rocks in lieu. What works best are hard (I know it sounds weird saying use a hard rock but some rocks are crumbly after a few months of washing) and jagged, not sharp but textured. I sometimes use a second rock to wrap the object I am washing in and rub the two rocks together. I guess this is a bit rough on the clothes or diapers but it works to get things like tar or pine pitch out of fabric when soaking just seems to set it more...
For soap I use biokleen or ecover laundry soap or dish soap. Usually when I run out of laundry soap I will use dish soap till I run out of it or I will use laundry soap to wash my dishes sometimes, lol.
Wrining is what really gets me too! This summer was so dry and hot I didn't even bother with wringing out clothes and my hands thank me for that. I am considering investing in one of the mop buckets so just incase I end up hand washing again I will have a solution to wringing that won't drive me nuts!