What is the best way to clean up dog hair from... well, everywhere?

Bet Hi,. Try the vaccum, with different tools. Aloha!

the disposable 'Swiffer works well on hard surface floors; a sponge mop, squeezed almost dry will make hair roll up from carpet -- if it's from a long haired dog; a very STIFF 'scrub brush' type broom works well on plush carpet for short hairs, for a woven pile rug - if an area rug vacuum from the BACK side ... on furniture a damp sponge will remove hair from long coated animals ... short haired dogs ( Doberman, Dalmatian, Greyhound, have a microscopic 'hook' on the root end of the hair that works it's way into the fibers of rugs, etc.

REGULAR grooming of your dogs ... weekly or more often will lessen the shedding and control where it goes ( into the brush you are using! not on the floors ). for short haired dogs, a natural bristle hair brush or a 'hound glove' works beautifully --- for long haired dogs, learn to remove the undercoat that creates the 'dustbunnies' and what we call 'foofballs' by using a technique called 'Line Combing' --- some good YouTubes can show you how....

For fabric surfaces, I like a lint roller for what the vacuum doesn't snag.

You came to the right place! My girlfriend bought this set:

https://www.qvc.com/qvc.product.V34207.html?colorId=011&sizeId=000&ref=GBA&cm_mmc=GOOGLESHOPPINGFEED-_-GShopping|M|Generic|home+improvement|vacuums+cleaning-_-pla-_-sa3ZnpVEK|dt_44906292707_413815169965__V34207-011-000_&mkwid=sa3ZnpVEK|dt_pcrid_44906292707_413815169965_pkw__pmt__productid_V34207-011-000&gclid=Cj0KCQjwgOzdBRDlARIsAJ6_HNlaZsQHVyiDvIfbStcnDIahfEyCEyKyWHEgeHMCQU-g8ehbK2ddr_IaAh3YEALw_wcB

I was dubious until I used it and then ordered my own set. Works like a charm! You don't have to purchase from QVC, there are similar brands sold in stores everywhere.

I have 3 dogs, 6 cats, a canary and a dragon + the neighbors 3 dogs plus any visiting pets. I vacuum every single day. Without fail.

A damp sponge works well nearly anywhere.