So in my particular case I don't cook with any animal products and when I'm washing my pots/pans/dishes I feel like I'm wasting water. Is there a way to not waste as much or is there a way to reuse that water?
Best thing we've discovered is using our faucet's "spray" setting 100% of the time when we're not filling up a glass or a pot. Our faucet has a button on top,
like this one.
-Water comes out at higher pressure, doing a better job on dishes
-Water comes out over a larger area, doing a better job wetting things or rinsing things
-The volume of water coming out is much, much less
We typically will turn on the sprayer once to wet something down well. Then have at it with a few drops of soap and a
good scrubby brush, with the water off. Then once more back under the sprayer to rinse all the soap and any loosened crud off. Then, off to the drying rack. Total water consumption is absolutely minimal - basically two 5-10 second bursts to wet down whatever I'm scrubbing.
EDIT: I couldn't remember the name of this technique, so thanks to vhalros. This is basically a 'navy shower' for your dishes. No reason to submerge them under a stream of water for minutes on end or have a huge bathtub of water you dunk them in to attempt to clean them.
Beyond that, try getting in the habit of immediately rinsing things off that you cooked in - you won't need to soak them later, even though you will need to wash them with hot water and soap. For stuff going in the dishwasher, if you're not going to run it soon, give it a quick
scrape and rinse before it goes in so stuff won't crud on badly.