First, and foremost, the primary goal for a young child going fishing is to have fun--- not catch fish. Some adults have trouble remembering that.
Take them to a pond, lake, or small stream where the panfish are plentiful, and fish with live bait and the simplest of gear, such as a cane pole or spincast outfit. Also take a bucket or two, and maybe some jars with holes in their lids. Don’t try to fish yourself. If you do, you’ll just get frustrated. Your full attention should be on being a teacher.
Remember that most every child will want to keep the first few fish that he or she catches. It’s natural, perhaps that first awakening of the hunter-gatherer imperative that is a part of our species. If the fish aren’t biting, that same instinct will kick in when the child turns attention to catching frogs or crawdads.
Before you respond to a plea to keep the catch, start a conversation about its color, size, beauty, and/or uniqueness. Point out a frog’s webbed feet and its big, flat ears on the sides of its head. Spread a sunfish’s dorsal fin and explain its spines. Hold your hands up vertically by the sides of your face and wave them back and forth as if you are a fishing breathing through gills. It’s okay to be silly. Actually, it’s better to be silly.
Suggest placing the critter in a bucket or jar, without agreeing to take it home. Usually, that will be enough. By the time that you are ready to leave, the novelty will have passed, and you can turn loose the catch without protest. I’d suggest doing so with a little ceremony, maybe waving goodbye as the fish swims or the frog hops away.
If you meet with resistance, explain that the animal will die if taken away from its natural home. Most kids don’t think about that until it is explained to them.
When the time is right, too, keep some of those fish and teach kids how to clean them.
Above all, though, take them fishing.