There are no easy cheap ways to create a greywater system - they are very complex to do properly.
- You need a storage tank with a filtration system and typically is not cost effective for the little bit of water you will be collecting.
- If not done properly, soapy water can become septic very quickly and when you water your lawn, you will be using very smelly water and will not want to enjoy your yard.
- If you want to use second hand water on your lawn - look into a rainwater harvesting system.
If you want to use less water you are better off just using less:
- low flow faucets,
- low flow toilet,
- low flow showerheads,
- on demand hot water recirculating pumps,
- water efficient dishwashers and clothes washers,
Water leaks account for the majority of our water waste - be sure you control your leaks including your dripping faucets and running toilets.
For more information:
Also, read Randy Potters's Q&A "Is it feasible to reuse greywater as irrigation water?"