Do not put shampoo on your garden. Shampoo contains industrial degreasers, unwanted salts, bleaches, thickeners, perfumes, colorants and preservatives. The cheaper the shampoo, the nastier the ingredients.

If you want to use the no-dig method, you really need to start, paradoxically, by digging your soil over, just the once. Following that, you need to apply far more organic matter to the top than you would were you digging it in. You need to add layer on layer, year on year. It can be fantastic, but only if you have a huge supply of good organic matter. A really good mix would be old straw (from a good, chemical-free source) mixed with liberal amounts of horse manure, stacked up for a month to rot down first. Absolutely no sawdust or wood shavings from the horse bedding. Newspaper is next to useless, and newsprint contains noxious chemicals. It's OK for keeping the frost off in emergencies, but that's it. A good thing to do is to add THIN layers of grass clippings regularly through the summer. When weeds grow, pull them out and leave them on top to wither away on fine days to add their goodness back to the soil.

If you can't get access to huge amounts of organic matter, no-dig isn't really for you. You can mess about with plastic sheeting and old carpet, but just think how horrible your veg plot will look. If your garden doesn't look very nice, then why would you bother?