The only thing you need is fabric and/or scraps which you sew together, maybe on a larger piece of waste cloth - and some kind of batting: in this case I recycled an old mat from my ironing board, but instead of buying new interlining you could f.e. make use of a worn-out sweater, a towel or a thin blanket - or several layers of fabrics you want to get rid of :-).
A pair of old jeans would make a wonderful big basket for toys or even fire wood, I think!
Anyway, you should end up with a rectangular piece of scrap fabric, fold it in the middle and sew the short ends together to receive a kind of broad pocket.
The trick about producing a basket or a bucket out of this is to sew a seam in a right angle across the edges to achieve a bottom - this is also often used to get that third dimension to bags of all kinds.
If you feel you need a solid pattern to do this, you can buy one from one Etsy (one example is designsmayamade, who makes them out of burlap and with handles) - and if you just want the buckets without having to sew yourself, I suggest you visit the shop of roxycreations.
(German summary: Mir gefällt die Idee sehr gut, aus Stoffresten auch Behälter nähen zu können - Behälter kann man ja immer brauchen. Der Trick ist, einfach die Ecken großzügig im rechten Winkel abzunähen, um einen Boden zu bekommen - ähnlich wie auch bei Taschen aller Art.)