Build two temporary walls, one on either side of the removed wall, by securing 2x4s to the floor and ceiling and inserting a stud between them under each joist.
Cut the studs 1/8 to 3/16 inch longer than needed, says This Old House general contractor Tom Silva, and wedge them in place with a sledge-hammer. Then call a contractor or engineer, who should be able to cut back the joists and install a beam in the ceiling, at which point you can take down the temporary supports and enjoy your open floor plan.
How to keep this from happening to you: Do your detective work before you demo the wall. For the most part, an interior wall is load-bearing if it is perpendicular to the joists or rafters above it, rides directly over a basement beam, and has an exact match on the story above and/or below.
If you're unsure, hire a contractor or engineer to look at the house, or take the blueprints to your local building department for assistance (and be prepared to apply for a permit for the removal job).
