Upon seeing craftknowitall's reusable Swiffer cover Instructable, I was inspired to do the same - it was one of those perfectly logical why-didn't-I-think-of-that solutions. After I finished one, though, I also thought, "Why does it need to fit a Swiffer in the first place?" Thus, after thinking of alternative handles and other such details, I sewed this as part of my continuing effort to reuse more and dispose of less while at the same time saving money!
If you prefer the Swiffer handle, I whipped up a printable, to-scale version of craftknowitall's pattern uploaded here as the original version. However, I found that the handle we had required different measurements, and I adjusted her pattern to the modified version which fit mine. To make it convenient to flip over so you can use both sides equally easily, you might also just completely exclude the portion of the pattern for which I wrote "cut only on top layer".
Step 1: Materials
A handle such as a paint-stirring stick or ruler (preferably flexible)
Anti-pill fleece; normal fleece may work but I haven't tried it and the price difference was minimal
A sewing machine and thread
A marking tool such as a washable highlighter or marker
Step 2: Design Considerations - Get a Feel for Your Fleece
On one hand, you want the fleece to flop around and thoroughly dust uneven surfaces, but on the other you don't want it hanging everywhere and being unwieldy. Before cutting anything, try holding it with different lengths free to decide how long you want the dusting strips or "feathers" to be. I went on the long side with 2 inches and think anywhere between 1 and 2 will probably be fine.
If your fleece won't stay on your handle, a simple solution would be to cut out a space to insert a clip such as a clothespin.
If we use the minimum of two layers we'll have a fairly flat duster which works fine or most purposes, but it would be good to have something a little more robust. I used two more layers, with the top and bottom layers narrower than the middle two so that the middle layer dusting strips would be able to hang out over the layer beneath.
Step 3: Lay It Out and Cut It Out
Trace the handle onto your fleece, measuring out the length of the dusting strip on either side of the handle so you have enough room for everything. Be sure, of course, to leave enough room for the part of the handle you'll hold. Do this twice to make the inner two layers.
The procedure to make the outer two differs only in that this time you won't accomodate the handle; essentially, these layers will consist entirely of dusting strips. Trim these layers to be smaller than the middle layers according to your preference. I think between half an inch and one inch is good.
Step 4: Sew Them Together
The trick here is to sew the top and bottom layers respectively to the middle two layers before sewing the middle two together. First, simply align the top/bottom and middle layer so that they share their lines of symmetry and sew a straight line down the middle for each pair.
When both are done, join the two middle layers by sewing along the handle outline you traced. Try to make it a close enough fit that the fleece won't slip off the handle, but don't risk not being able to fit the handle in.
Step 5: Cut the Strips
To get the greatest possible range of dusting, cut the strips almost all the way back to the seams you sewed. The width of the strips is again a matter of user preference; I went with half an inch. If you arc the end like I did, the ends will probably be awkward to work in. I recommend quickly sketching out your intended cuts first to make sure they'll be wide enough at the base not to rip off but not so wide that their outer ends are outlandishly large
Step 6: Try It Out!
I had both cloth fuzz and conventional dust in the vicinity when I finished, and it passed the first test with flying colors! I've heard that it's best not to use dryer sheets with these as the resulting static electricity helps attract dust, but I don't use dryer sheets anyway. To help increase the static charge, you could try touching it to the appropriate materials - my fleece is polyester, so referring to the triboelectric series, I know that fur, glass or my hair (as long as the duster's clean) would be good choices. Thanks for reading!