It's slightly adapted from the organic gardening handbook. IIRC they put the manure down first, but then you'd have to punch holes through the cardboard to plant the spuds, and the weeds would come through the holes! So I changed it, but I'm sure I've read somewhere else of putting the cardboard first.
I think the benefits are only to the individual, I don't have any basis for comparison yet though.
Harvesting is easy too, as the spuds are either in the straw or just on the surface of the ground.
So lazy beds are a bit like raised beds without any formal wooden edging - have I got that right?
That's how I would describe them except that 'raised beds' seems inextricably linked with wood in most peoples' minds.
I usually refrain from posting my opinion of the wooden version as they are so popular, I just chip in with 'lazy beds' whenever I'm not too late.
For some reason almost everyone seems to jump straight from the idea of traditional big beds with everything in rows to wooden raised beds, when in fact there are other options. No-dig beds don't need to be raised at all, but have a lot of advantages. Raised beds or lazy beds are only really needed if drainage is a problem. I see the wooden walls as unnecessary, and environmentally unfriendly, and they almost invariably lead to the need for tons of topsoil to be trasported in. On a more personal level they are more work, and will eventually need replacing - more work again. They are also immovable, and provide hiding places for slugs and snails and weeds. (Try digging up bindweed from under the edge of a raised bed!)
I have quite a lot of experience on clearing and preparing ground, and general gardening, but when it comes to veg I am a beginner. If you ask me which is the best way to grow a veg, I won't know the answer. (e.g. spuds as above)