My original encounters with eels were not pleasant. My mother, fond of roasted eel, liked me to catch them for her with a drop line. All the other fish I hauled onto the dock flopped about and died of natural causes. An eel, however, was a living breathing nightmare. It failed to drown in the air, so I had to bash it over the head with a hammer.
It turns out that eels breathe air because they hatch in the Sargasso sea as little translucent elvers, then journey up fresh water rivers to grow for thirty or forty years. There they can travel by braiding themselves into balls and rolling over mud flats, breathing for a few minutes. Sometimes they burrow down in the mud for the winter. The Patuxet caught them by wriggling their toes in the mud, a technique Squanto taught the Pilgrims after their first terrible winter.

Nature Writer Jerry Dennis notes that “Naturalists eventually realized that the large dark eels of American and European rivers and the smaller, transparent eels known as glass eels or elvers that were sometimes found in estuaries were actually different stages in the life of the same creature.” Jerry Dennis, A Walk in the Animal Kingdom.
In my invented worlds I sometimes use details from my research rather than from my personal experience. That is how I learned about eel sticking. Fen folk look for telltale bubbles in the mud, then stab straight down with long spikes, sometimes getting into contests to see who can catch the most:
“…two figures were silhouetted on the farther shore. They were facing the other way, spears held aloft, eyes on their feet. They were eel stickers; they looked for bubbles, then pounced swiftly to impale their catches. They were having a contest, as eel stickers were wont to do. Faint cries of triumph traveled over the water as they called their scores to each other, tossing eel after eel into baskets slung from their shoulders.” The Marshlanders
If all else fails, I learned, you might come across a heron with an eel stuck in its craw.
Here’s what to do:
“A heron stood by the shore not far from their longboat, swallowing an eel. His catch wasn’t going down his throat; it thrashed madly, half in and half out, while he tried to eject a dinner that had turned into a threat. This, too, had come up in their training. Clare ran in front of the heron, which startled backwards just as William grabbed it from behind…Remembering to be gentle, Clare massaged the bird’s feathery gullet with one hand while pulling at the eel with the other. Suddenly, she fell back on her rear end with a shout of triumph, holding the flailing eel.” The Marshlanders