Second the idea of baby-led solids. We've used this approach with all three of ours now and it's a good way to side-step the stress and struggles. And we do feel that solid food is mostly experience, not nutrition, for the first year so that shapes our approach as well. The Dr Sear Baby Book is another nice source (Our Babies rocks though) and the Kellymom page linked above has dozens of links about introducing solids.
Anyway, since we're feeding our littles directly from the family plate there is less mess... while it's easy for a child to "throw" an apple or sweet potato wedge it doesn't have anything near the mess potential of applesauce or sweet potato mash!

So I think a lot of mess control comes from offering non-messy items. Three or four cheerios or rice puffs is plenty for exploring sensations and pincer grip and there isn't a lot of mess even if the whole thing gets dumped on the floor. Softer foods that do have a bigger mess potential get doled out in smaller amounts... avocado pieces or banana pieces often get served in mesh feeders (easier to get a grip on them) or if they've been mashed then just a small scoop goes on ds's plate. If I need a few hands free minutes I'll give ds a mummum or teething biscuit, but in general he sits on an adult lap or we all sit on the floor picnic style and hand him things to nibble.
And, well, I generally serve messier things right before the nighttime bath so if oatmeal goes in the hair there's no harm done. (actually, we used to strip dd1 down to a diaper for dinner since she was determined to use her own spoon from the start and a 7mo with a spoon is a force of nature... but even then there wasn't mess everywhere. It was just on her

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I think a certain amount of mess is normal during the early days of self feeding. Just like a certain amount of spit up while getting the hang of nursing, or a certain number of tumbles while learning to walk. The kiddo is figuring the whole process out and working on a whole new skill set. But by offering foods with a lower mess potential, or offering smaller portions, and waiting till they're really on top of the physical skills necessary I don't think you need to expect the sort of food-pocalypse cartoon image.