Sweeping & dusting pick up some hair, but spread a lot around and miss a lot, too. The ultimate answer is vacuum, vacuum, vacuum. Vacuum the floor. Vacuum the furniture & tables. Just vacuum everything! I have a dyson, which "sucks" really well, but it's pretty cumbersome with the hand-held attachments, so I supplemented with a Shark bagless lightweight vacuum. Sucks up very well, too, but the cup is small & needs to be emptied after a couple of minutes.
All mine are shedding much more than usual lately, but Henderson (corgi) is out of control. I brush him, furminate him, etc., etc., but the hair just keeps on coming. And he's brown & white, so it shows up on whichever surface it's on. All the greyhounds and cats I've ever had all rolled together haven't generated as much hair as this one little corgi! (They TOLD me corgis shed a lot, and they really meant it! )