My daughter really was the same way. I worried about her, but her pediatrician assured me that her body would tell her to eat and not let her starve, even if it was less than a teaspoon of food! He said as long as she was healthy and maintained her normal activities she was fine. She actually was this way from about 18 months to 3 1/2, then started eating better and although she is a picky eater, she has never gone back to not eating. For her I think it may have been a part of her "terrible twos" which coincidentally were at the exact same time, she started early and ended late :-/
My advice is to just place her food in front of her, using smaller plates (I sometimes use saucers for my little guy) let her see the rest of the family eating and enjoying their food, and she may or may not try it. Just pick up her plate at the end of the meal with everyone else's. Don't let her fill up on liquids before or during meals, but make sure to offer her milk if she doesn't eat a meal, at least that will get some nutrition into her. Don't offer junk food between or at meals, concentrate on offering healthy whole foods. Ask her day care what exactly she's eating if you don't know, and try that at home. If she doesn't eat it when you prepare it then it is a control thing, and I would just continue to offer but not try to get her to eat, no coaxing or bribing (NOT that I think you do) so she feels she's in control when she does eat.
Right now I'm having difficulty with my guy who's 27 months. He's working on getting molars in and along with the hot weather he sometimes will only drink cold milk and water. But he's doing everything he normally does even when he's not eating, so he's OK.
Hang in there, mom : )