Here is a video that provides an example of a way to do dishes using a very minimal amount of water. Throughout the month I have budgeted myself only about a litre to a litre and a half of water per day for dishes, which believe it or not is very doable! Check it out for yourself!
*note* using a dishwasher is generally more water efficient than washing by hands if you always load the machine full before running. A dishwasher will use about 15-25 litres of water for the same size load that a handwasher will use about 50-60 litres for. However, with the method used in the video, you can wash the same amount in under 4 litres.