The grocery store would only be liable (or legally responsible for your costs and/or injuries) if they were at fault--they are not liable simply because you fell on their property, any more than you would be liable for a friend's injury if the friend slipped and fell at your home without you doing anything wrong.They would be at fault if:1) They actually knew of something wet/slippery on the floor (such as because someone had told them), had enough time to clean it up, but still had failed to clean it; or2) They *should* have reasonably known that something wet/slippery was on the floor, such as because enough time had passed that they (some employee of theirs, that is), should have spotted it, and again, had a chance to clean it, but failed to do so; or3) Some employee of theirs caused the wet/slippery spot.If they were not at fault--for example, if a customer spilled something only a few moments ago, and they did know of the spill or have any chance to clean it up--they would not be liable; without fault, there is no liability in a case like this.Even if they are liable, if they will not voluntarily compensate you, you would have to sue them for the money; to win, you'd have to be able to prove in court that they were at fault.