Many of my lampshades are made of different types of fabric, which accumulate dust. I've tried wiping them, vacuuming, etc, but I haven't been happy with the results.
What can I do?
You can get a length of clear packing tape about 8-10" long and, holding the ends, press it against the lampshade and draw it back off. It will have picked up the dust in that area. Then press it on another spot. Repeat this process until the lampshade is clean.
Unless it's very dusty, the tape usually lasts a good 2-3 shades for me. Once it is no longer sticky enough for use I cut another piece.
Similar to your suggestion of tape, but probably easier and quicker is to use a lint roller like this:
A lint roller has a roll of masking tape on it, and is usually used to remove lint from clothes. But you could also use it to remove dust from lampshades. Just roll it on the lampshade and it will pick up the dust. Then after the tape loses its stickiness, just tear off that piece (they are pre-cut into squares on the roll) and it will be ready to pick up lint/dust again.
The brush-end of a vacuum's upholstery cleaning attachment works great.
Attach it to the hose (and extension, if necessary) then starting at the top of the shade, use straight, gentle stroke all the way to the bottom rim.
Turn the shade a tiny amount -- or move your body around it -- then repeat in slightly overlapping swaths until you've completed the entire diameter.
Lampshades are very difficult to dust. They contain nooks and crannies which make it impossible to really get in there and clean them thoroughly. They are also fragile, so you can't wash them off using water, detergents, etc. Most vacuum cleaners would also damage them unless you have a soft brush attachment.
One of the best ways to dust them is to use a can of compressed air. This is the same kind of compressed air used to clean out electronics, and most office supply stores carry them. Work back and forth, and up and down across the entire shade and make a couple of passes. This should remove the vast majority of dust.
This may seem like an "old-fashioned" solution, but have you tried a simple feather duster? I have a cheap one like this, and find it excellent for getting dust off lampshades.
Of course, the feather duster will mostly just scatter the dust into the air, so you may want to hold a vacuum cleaner nozzle nearby to collect it. Or just let it settle, and then vacuum the floor.