I know someone who has great difficulty observing Shabbos correctly, because she is very accustomed to using a sponge to clean dishes, and a sopping wet rag to clean kitchen surfaces (which are constantly getting very dirty due to serving several children food throughout the day). Leaving the sink full of dishes, or leaving kitchen surfaces dirty, are not acceptable to her because it is disgusting. Using a Shabbos scrubber with cold water doesn't wash dishes well enough for her (it doesn't get off fat or oil, for one thing). Just placing everything in the dishwasher is not a solution, because they need to be cleaned somewhat first for the dishwasher to be effective (requiring the sponge), and because many of her kitchen items can't go in the dishwasher.
My question is: How, as a practical matter, do people who are fully Shabbos-observant deal with cleaning kitchen surfaces or washing dishes on Shabbos without violating prohibitions such as squeezing and using the hot water faucet? Given the information above, how would you advise the person to transition to observing Shabbos while keeping the kitchen as clean as she likes?