Offer one bite at a time. Fill your plate with pieces of fruit, veggies, or other cut-up morsels of food and sit next to the child. Offer him one tiny bite at a time. When the child finishes that bite, offer another. Sitting a toddler down to his own plateful of food is inviting a mess.
Laughter is messy medicine. Babies are born clowns, and this especially holds true at the dinner table. Laughing at baby's messes will only invite an unwanted encore. If there are older children around, they'll often enjoy (and encourage) baby's messy eating antics because they don't have to clean up the mess! The choice is either to enjoy this home entertainment as a passing stage (which is what I would advise) or insist that your "audience" help clean up afterwards.
Control the mess. If mealtime gets out of hand, end the meal -- and the mess. In our family, we would allow a mess on the high chair tray, but completely discouraged food flinging and purposeful dropping by immediately terminating the meal. Once baby understands the effect of her actions, the food will stay where it belongs.
Use utensils to distract. Our daughter, Erin, used to windmill her arms during feeding, causing food to fly everywhere. Our solution? We put a plastic spoon into each of her hands to occupy her while we fed her with a third spoon. You can also try placing toys with suction cups on the highchair tray and letting the child play with them while she's fed. And of course, there is the tried-and-true spoon-airplane trick -- food will land safely into baby's eager mouth while keeping her entertained.
Drink up. If most of the meal makes its way to the floor rather than to baby's mouth, serve up smoothies in a tightly-sealed sippy cup that she can drink to her heart's content. (You can also use a bendable straw in a pinch.)
Use a sit-still strategy. Some toddlers kick, squirm, and make a mess simply to get out of their high chair during mealtime. To settle our own little squirmers, we used the rapid-fire feeding trick: we would keep coming at that little mouth with a small bit of food. Our kids would be so busy trying to keep up that those annoying kicks would soon cease.