Like most people I am not a fan of dusting, but I hate dust so I have to do it. There is no easy way to get rid of dust. I know there are blowers and canned air, but that isn’t really cleaning up the dust, that is just moving it around. The main thing I have to dust is shelves, so the best method for cleaning them is by wiping them down with a wet rag. It collects all of the dust and doesn’t spread it back into the air. I use the same method on other items that won’t be ruined by water. And if it can’t be wiped clean and won’t be ruined by water I am not opposed to rinsing it off in the sink or with the hose. There are also various wipes that achieve the goal.
I like the wet rag method because it is simple, effective, and doesn’t require a lot of extra cleaning supplies. For the items you can’t get wet, there is always the classic feather duster. Some of the modern designs are pretty nifty and are made to statically attract and trap dust. You can also use a dry cloth to wipe down your items.
For getting dust out of carpeting and furniture, you are still best off vacuuming. Baking soda is a good attractant for pulling dust and hair loose, so it can be vacuumed up more effectively.
Ideally you want to look for methods that collect and remove the dust. Compressed air and cheap dusters just blow around the dust, putting it back into the air for you to breathe. This can trigger allergies and other irritations.