My kitchen is going through a renovation and they are tearing down the
walls and ceiling.
There is a fine dust residue all over the floor and stuff in the basement
below.
My regular vaccuum cant handle the fine dust.

Don't use any conventional vac to suck up drywall dust. It will damage the
motor (and most likely blow right back out the exhaust port).

With SOME vacs, you can BUY a special VAC FILTER/BAG MADE SPECIFICALLY
FOR DRYWALL DUST.

If the floor is not carpeted, damp-mop it. Likewise dust the objects
with a damp rag. Rinse the mop and rag frequently...Yep, thats it

If the floor is carpeted, try to get a hold of a shop vac.

Not unless the Shop Vac has a DRYWALL filter in it. The "Shop vac DRYWALL"
filter bags are YELLOW vs the Normal white.