If you looking for a quick and easy non-long term solution, then take some 2, 4 or 6 mil plastic tarp and staple it to the joists. True a drop celling or drywall would be the preferable solution, but the tarp will solve the immediate problem. You should be able to get a 4 mil 10x25 roll for around $10 - $15 depending where you live, and it's something you can do yourself in just an hour or two. Later, with the available funds you can get a celling or drywall up.
Now the tarp will act like a vapor barrier, so don't trap the air between the joists at the ends, or you may find your trapping moisture along with the dust.