I have 9 cats, several of them very fluffy. They generate quite a lot of fur.

First, I keep cat grooming brushes everywhere I spend much time (desk, couch, bed) and when a cat is within reach I brush them. They enjoy it greatly (can take some training, and some of them only like it on some body parts) and it helps enormously with reducing the amount of fur that ends up here, there and everywhere (also it makes petting them nicer as they shed less when stroked).

Incidentally, if you keep the fur collected by the brush it can be felted into toy balls or other items (see “Crafting with Cat Hair” and other cat fur crafting guides), and if you want to make a drop-spindle you can spin it into yarn that you can knit with (this works best with long-hair cats and underside fur which is softer and more flexible than the topcoat).

Second, I have no carpet anywhere in the house, so fur that the brushing doesn’t get tends to collect as fluffy balls in corners where the air currents push it, so my regular sweeping and vacuuming pick it up easily.

Third, I have low-nap area rugs in a few rooms. Loose fur tends to collect on them much more than on the bare floors, which tends to reduce the amount of fur loose in a room, and vacuuming them frequently is faster and easier than vacuuming the whole room (I usually vacuum the rug, then use the hose attachment to quickly run around the perimeter of the room to collect fur and other dust.

Last, select a clothing washer that does a good job removing fur from clothing. In my experience front-loaders that use minimal water are pretty terrible at removing fur, it just gets balled up and sticks to the clothing. I prefer top-loaders that use plenty of water as they seem to do a better job removing fur. I know that increases water use, so it might not be desirable in some locations, so if you are in a place where water use needs to be restricted it might be worth doing some research to discover what low-water machines do the best job with fur.