For the patio box, I recommend a 1/4" thick piece of plywood with holes drilled in the middle of each square with an extra one in each corner.

For the other boxes, cardboard will smother the grass and weeds that are already on the ground when you wet it down and add soil, but after a while it will decompose and the roots will be able to grow downward as they please.

Hometherat is spot on. Plywood is great for the patio box, but don't forget those holes.

I have it different ways in the garden itself. My first boxes have landscaping fabric. This fall, when I tilled in some more compost, I took the rake down there and lifted off the fabric since what was under it originally was now long dead. In other boxes back there, I have cardboard. Both will do equally well.

thank you guys so much!

I think I am going to go with the cardboard, I have some old boxes I need to be rid of in the garage anyway! (kill two birds with one stone!)

We have gophers so we attached chicken wire to the bottoms of our beds using U-shaped carpet tacks. This totally prevented the heartbreak I had previously growing in-ground when whole plants would disappear.

Then you can set the bed on top of any weed block, like you normally would.