get some 5 gal buckets, or some larger rubbermaid containers, remove the live rock from the tank, putting the rock in a container under water will minimize some die off, and you can put a power head and heater in the containers to keep water moving while you set the tank up. I would take as much water as I could, but if you keep the filter media which has beneficial bacteria in it, you will most likely be able to mix up some fresh saltwater with out setting off a full cycle, it would be similar to doing a large water change.
I would suggest placing the fish in a separate container from your LR, it will keep the rock from shifting in the moving process and crushing a fish.
Since you are talking about cleaning the tank, the best idea would be to remove the substrate (what is the substrate? Deep sand bed, shallow sand bed?) and to wash the tank using a water and vinegar solution (figure approx 1 part vinegar to 10 parts water) and if the tank is glass, i would also use a scraper to scrape any film off of the glass. Rinse the tank out very well to remove any residue from the cleaning process.