Whats the easiest way to fix sticky painted furniture so that it's no longer sticky?
It's called "blocking" and often happens w/latex paints - especially if the 1st coat wasn't allowed to dry fully before the second coat was applied. It's not much of an issue on walls, but horizontal surfaces are a different story. 

The ultimate solution is time - possibly a few months. The inner coat's moisture is blocked from evaporating by to outer coat. It will slowly wick through the surface over several weeks. 

You might be able to reduce the stickiness by spreading some fine talcum powder on the surface, then lightly vacuuming it off - but TEST in an unobtrusive area, first, because if it's too sticky, you could end up with permanent, visible, dust built into your paint job.

You may be able to speed the process by blowing warm (not hot) air across the surface for several days (hot air can cause the paint to peel). This can open the pores in the paint to allow slightly more rapid evaporation, but a lot depends on what paint you used, how much moisture is trapped in the undercoat, etc.