I've unpacked a few of my models after moving home some time ago, these models have been in a cardboard boxes for several months and need cleaning:
I've tried compressed air, which only makes some of the dust airborne. I've also tried cotton buds but the process is tedious and they end up looking like this after several stokes.
More importantly, I would like to be able to clean my models without going through the tedious process of taking them apart, washing, drying and building them again.
When cleaning dust from scale models, sculptures, figurines or LEGO models I use an artist 'Fan' brush. This is the best method I've found to clean dust rapidly without damaging models.
The fan brush's long hairs combined with the thin spread enables you to dust 'any shapes and surfaces without risk of damage. For example, it would clean a LEGO antenna (1 stud attachment only) without making it fall. You can can really push the brush into the bumps and cracks and the long hairs will bend and reach around the features.
Also, when dusting a big piece, I also set an electric fan a low power to blow air across my work table. This prevents the dust from just going up and settling back down on the model.
A huge advantage, learned after cleaning model boats, is that it is also perfect for dusting ropes (small cables). This worked like a charm on my LEGO Technic crane with all the complex cable system. It is also good on cloth, so it would work for the minifigures capes.
Have you tried one of the smaller portable vacuum cleaners? I've had a few of the battery operated "Keyboard Cleaner" type of thing, which usually come with a brush nozzle and work quite well.
Unlike firing compressed air and scattering dust/crumbs/contaminants everywhere, they are designed to catch most of it.
Faster than doing it by hand with a tooth brush or cotton bud.
I've successfully used a paint brush to clean my dust-covered MOCs.
A soft toothbrush can do a good job on an assembled model. Just make sure the bristles aren't too stiff. They could scratch the elements. It's still tedious, but easier than cotton swabs.
Try the cyberputty gunk that picks up dust. it's basically silly putty but it does what it says it does. I use it for random things like this all the time. Radioshack has it for $1.99 last I saw.
I use a static duster for dusting models. They use soft polyester filaments that won't scratch, and which attract dust using static charge. It may take a few passes to get all the dust if it is thick, but they work well.
Most of the answers here use various combinations of air and brushes to get rid of dust. This works fairly well; I used to dust my model airplanes with the same paintbrushes I used for painting them. I second the tiny portable vacuum cleaner too.
However, my go-to option for dusting models that have been standing around too long is soapy water. I recently partially disassembled the 4483 Lego AT-AT that's been standing on my desk for years. Pop the legs off, the head off, and the panels off the top, etc; it comes apart into, say, 10-15 large modules. Dunk them in soapy water then rinse in warm clear water, and let it dry. It takes a while to dry but when it's done, it's clean. Much cleaner than the dusting approach.
I've washed individual pieces this way too, by putting them in a mesh bag (like the kind for washing delicates in a clothes-washing machine) first, then dunking the whole bag of parts into the water. It takes a while to dry though.
My personal favorite method is using a submerged toothbrush. It works much better than any other method I've tried, as the brush dislodges the dust and the water ensures that the dust does not fall back.
I just use my Dyson DC39 vacuum cleaner with either the crevice or dusting tool. As long as you're careful, this works well.
