If you dig out a small pond how does it fill up with fish?

You have to stock it with fish yourself.
Wild ducks might find it if you live in an area with a roving duck population.

Bentonite, SoilFloc, or around here we use lime and/or pigs.

If there’s no waterway, like a river or stream, feeding your pond, then yes, you have to buy the fish, or transplant from a local waterway, maybe even contact your conservation dept.

Sometimes ducks, geese and other animals will come to a water source on their own, but you can purchase them as well.

It is possible for fish to show up in ponds which have not been stocked. Eggs can get stuck to the legs, head, neck of birds feeding from other ponds, lakes, etc. If they are not dried and dead when the bird gets to another location, they can naturally stock a pond. Of course, if there are not both genders surviving to grow, it won’t stock the pond.
Another way is an even less likely long shot.
Tornadoes have been proven in rare cases to pick up fish and frogs, and dump them somewhere else.

They might migrate in floods from heavy rain.

That’s impossible, someone has to put fish in the pond.
On the other hand ducks somehow know where a puddle of water, at a shopping centre, is after heavy rainfall, is even if it’s far from a river lake etc. Why do they leave the natural body of water anyway?

…I just read @Patty_Melt‘s and @RedDeerGuy1‘s posts, so never mind re. “it’s impossible.”

We have fish around my area, called Mosquito Fish (not directly if that’s what they’re actually called.)
Their eggs get stuck to feathers of birds that get into the water. I believe that they eat mostly Mosquito larvae, which of course grow in any standing water. So… I guess Mother Nature have them the ability to follow the food….

Tilapia, Bass, and other fish can follow flood waters in, or be dropped by fish eating birds. We have LOTS of Ospreys around here.

Native fish can just show up. When I was a kid a neighbor had a pool that was unkemt and ended up with fish in it. Tons of frogs lived in it that probably inadvertently brought stuff from a nearby pond or Creek.

I remember a small pond that was little more than a large puddle had a couple little bass in it somehow.

Periodic or major event flooding can cause fish to migrate too.

@flo I just read an article about this is Smithsonian Magazine. Some fish eggs will pass through a swan’s digestive tract unharmed and will hatch in the water where the swan defecates!

Some poor grad student looked through piles of swan poop to identify viable eggs. Then they hatched them .

I stocked my pond by going to the local fish store and buying cheap feeder fish for 10 cents a piece.

The Ducks of course are no great mystery.

@LuckyGuy amazing. Never would have believed it.

@flo The study showed the swan’s digestive system is not very efficient. It lets many nutrients pass through unabsorbed.

@LuckyGuy Interesting. I wonder why they wondered?