Do you love big bluegill?
No, you're pretty much right; decay begins immediately after the bodily functions cease. And fish decay faster than other creatures. Knowing that, we attempt to delay or better yet, to control the rate of decay. The best way to do so is with cold.
Get the fish you intend to eat gutted, first, whenever possible. Do that at the waters edge, if practical. There are icky things in the guts of fish that are best removed ASAP, or they can spoil the flesh.
Then get the fish on ice right away, in plastic bags or on a thin mat of straw or dry grass. This keeps them from getting water logged in the ice melt-off.
If you are not going to eat them immediately, keep them as cold as possible like Bill does until you do consume them. If you are not going to eat them within a few days, freeze them.
Interestingly, while you dont want fresh fish gettin' waterlogged, it is best to fast freeze fish in lightly salted water. Place the cleaned fish in zip-lok bags with just enough lightly salted water to cover them. This prevents freezer burn and drying out in the freezer.