Good question, but in what context?
Backyard pond?
QT tank?
Fish dealership?
At the fish dealer, you can look for many things that might give a hint as to the condition of the livestock in general as well as a particular fish.
Dead fish in the tanks, on the ground, in view of customers? Not good.
Smells like the local bait shop on Sunday morning? Maybe not so good either.
Water clean? Funky?
Water at the dealer ought to be downright pristine, if its funky, not good.
Fish active? Swimming around? Looking for food?
If laying on the bottom with fins clamped, not good. If under the water inflow and never leaving, not good. If exactly spread out so that each fish is at the center of a space and no fish can touch another, very bad. Hanging head up, or down, bad.
Have the proprietor feed the fish so you can see them (it) eat. Does the fish actively pursue its food? Mouth not deformed (more common than you'd think and you see it when you get home and feed)? A healthy koi has a healthy appetite (unless its really cold). This can be the number one indication of a problem, not eating. If the fish won't eat, have the proprietor let it get hungry and have you back to see it eat at another time.
I know this is not possible at a show or in some other cases, but healthy koi ought to be hungry!
Body shape fusiform and proper for the size of fish? No lumps, protrusions, bends or deformities? No sores, red marks, bloodshot skin or fins?
Does the fish swim like it ought to? Tail swing both ways the same amount?
See any scratching or flashing with this fish or its tankmates? Not a good sign.
These are external, easy to see signs. Beyond that would be a microscopic examination, blood tests, etc. etc.
Brett