The basic idea: knit a rectangle. The width should be slightly narrower than the depth of the chair arm you're most often going to hang it on. The length should be long enough to tuck under the chair cushion for anchorage, come up the inside of the arm, over the top, down the outside to a level you can comfortably reach down to while sitting in the chair, and back up far enough to form a useful size pocket. Sew up the sides where it's turned up. Hang over the arm of your favourite chair, be sure inside end is securely tucked in somewhere, and install WIP in pocket on outside. If you have to move, carefully free the inside end and wrap it over and around the pocket to close it. Hang over arm of new chair.
To make the bag more stable, you can turn over the inside end to make a casing for a length of thick wooden dowel which you can really wedge into the crack at the inside bottom of the chair arm. If you prefer several smaller pockets to one big one, just run a vertical line of stitching through the pocket section to divide it. For a bit more technical interest, cast on at the bottom of the pocket and work both sides of the pocket together in double knitting. You can work in dividers by systematically swapping the yarns over at the same place in every row.
You can use any yarn and any stitch for this, but if the resulting fabric is not dense and tight enough to stop the stuff you put in it from snagging or falling through, you might want to make a fabric lining for the pocket. In fact, you could make the whole thing from fabric, in next to no time. Remember also that you'll be folding the work at the bottom of the pocket, so the back will become the front. Use a reversible stitch, or reverse the sides in your knitting when you get to that point, or use a stitch that looks good on both sides in different but obviously related ways - many of the Barbara Walker knit-purl combination stitches are good for that, or the slip-stitch patterns in the latest VK.
This can be as mindless or as fun as you like - let yourself play. (How about making one by sewing together swatches, so it served as a sort of stitch library as well as a bag?) If anyone does it, I'd love to know about it!