I (in the past with cats) have groomed the cats with a brush and comb regularly;
fed the cats foods that encourage a good coat and skin condition so that they didn't shed so much;
used a vacuum cleaner specifically chosen to pick up fur (in my case, it's an older-model Dyson with the "turbo brush" rotating head) and vacuumed a lot;
kept the cats off surfaces I didn't want cat hair on, such as my bed;
used a stick cat-fur-removing widget to remove the hair from some clothes if they got hairy.