Usually with my 16 month old daughter, when she starts throwing food over the side of her chair it is a good sign that she is done. You might try getting some easy-washed or disposable plastic/washable cloth that you could put on the floor underneath her high chair-- for example oil cloth, plastic tablecloths, or even a plastic shower curtain or garbage bag!
I have also found that at this age, it works better if I feed her multiple smaller meals rather than 3 big meals-- she just doesn't really have the patience (or the tummy!) to sit for a long time and eat. It also helps when I give my daughter a spoon so she can try to feed herself (though this doesn't help with the mess!), or give her foods for dipping, e.g. bread in hummus dip or something, which keeps her attention because it is a hand-eye coordination challenge, I think. She also is more "engaged" at meal time if she gets to eat what we're eating, instead of baby food. Just remember, she won't be little for long... you might also try throwing some food from your own plate onto the floor just to see why it's so fun... j/k!! :-)