9 out of 10 times, the mess is inside. Lift bottom, fold and dispose, clean and apply a fresh one.

That tenth time, I just found it easier to use a bath.

If it makes you feel better even sighted people don’t always do it without getting it everywhere, takes time and practice to build the skill of not bathing in crap lol

I guess if you're the parent who's at home dealing with the majority of the diapers this isn't practical, but since my wife changes most diapers and I only encounter dirty diapers occasionally when my wife is out, I just bath them. First I undress the child completely so nothing accidentally gets on their clothes, then I fold the diaper over the mess and wipe down with it as I go (I do all this on a washable changing mat which I wipe down when I'm done). Then I clean them with wipes the best I can in a methodical downward pattern; I use a lot of wipes just to be on the safe side. Then I bath the child. It's rather time intensive so might not be the best option if you're the one changing every diaper that comes along.

Also, my first child was a girl. Now I have a son and that's a totally different diaper changing experience. I stick a washcloth overtop of him while I'm wiping so he's not going to be aiming right at my face if he goes while I'm changing him (which has happened).

With practice.