I have a 6 year old that fishes with me regularly. I primarily bass fish, and my boy fishes for bass with some bass specific techniques and also with worms for anything that bites.
First, you need to get the rod and practice casting with him a week or two before you actually go fishing. I don't recommend getting a kiddy pole. They are cute, but they are nigh unto useless.
My boy had a zebco rod and reel combo from academy that was pretty nifty. The rod was I think 4' or 4'6" and the reel was a small sized zebco pushbutton. The rod is great, the reel didnt last but half a season, but my boy fishes hard.
For not much investment you can get from walmart a separate rod and reel. A zebco 202 reel is about 7 bucks. This lasted my boy about 6 months before it started having problems. He uses a shakespear durango rod from walmart which is 10 bucks. it's held up great. I think it's 5'6".
A bit longer rod like that is fine for a youngster, and actually I think it's easier for them because they have a bit more rod to sling a lure since their technique ain't as refined.
If you get that 202 reel, it will come with 10 pound line. 10 pound monofiliament line is a good all around line for normal fishing. It will handle anything in the bluegill, bass, crappie, and small catfish range. An important thing to consider is that you need to set the drag on the fishing reel so when you pull on the line it slips. That way, when you hook a huge fish, it slips the line instead of breaking the line. Pull it at the reel, not at the end of the rod.
So, then you need hooks and lures. For worms, you will need to get some aberdeen hooks. They are gold and about $2. Ozark Trails brand is acceptable. size 1 or 2 is larger, and size 6 is smaller. You want a pack of each.
When you hook the worms, you can do it several ways, just grab the critter and hook it through the center, then come around again and hook it through the center again about 1/2" away. OR, you can hook it a bunch of times, but this is more for catfishing. If you get huge nightcrawlers, cut them in half to conserve worms if you like.
My boy and I like digging worms, but we also will use store bought on occasion. Regardless, you must keep them cool. Put them in the fridge when not in use. If you go in 80º weather, they will die in an hour if in the sun. Put them in the shade when fishing, even your shadow when sitting on shore is enough.
Start with the smaller size and if you start gut hooking fish, which is when you hook them deep and cant get the hook out, then go up in size. If you do gut hook one, and you can't remove the hook, just cut the line as close to the hook as possible and throw the critter back in. It'll probably make it. Most likely you'll be catching bluegill or similar fish.
If you're in a place where you're catching bass, use the larger sized hook.
You need to know how to tie a fishing specific knot. Probably the easiest to learn and master is the Palomar Knot. It's also one of the strongest knots to use. It will take you about 10 minutes to learn and master it, including finding a suitable youtube video about it.
Get bobbers that are about 1.25" or 1.5" in diameter. I prefer the bright orange weighted bobbers. Weighted bobbers fly farther and easier, and stay in place in a light wind better. Put the bobber about 12" above the hook.
If you want to try artificial the easiest thing you can do is use a grub. A johnson beetle spin is hard to beat. You can use it with the included spinner and without. With the spinner on it cast it out, let it sink to the desired depth and reel it in at a moderate speed. Desired depth is... anywhere from 6" below the surface to 6" above the bottom. From shore, you'll be limited to shallow water. Whenever possible cast parallel to the shore.
Without the spinner, you can use the beetle spin in the same manner, but reel it back more slow. OR, you can let it set on the bottom and move it a foot or two at a time and pause a few seconds. Often times bass will hit it on the pause. You'll catch all sorts of species.
They come in various colors and weights. Get the 1/4 ounce size for large and 1/8 ounce for small. Black is the preferred color, though any color will work. They are about $2.
So next is setting the hook. When a fish bites the worm/bobber, the bobber goes under. The bobber will dance on the water when the fish are nibbling the worm, but when they get the hook, the bobber goes under. Set the hook as soon as it goes under. Don't jerk the rod, just pull back on it firmly.
For the beetle spin, you'll feel the fish "hit" it. It'll feel like a thump. When they thump it, give it 1/2 second, then set the hook. Again, don't jerk, just firmly pull up or sideways on the rod.
If you wait too long to set the hook you will gut hook them.
When you have a fish on, keep the rod at about a 10:30 position. Not flat, not vertical. Keep constant line pressure on them via reeling and using the rod. when they get to shore, leave about 5' of line out. Reeling too much line up makes it hard to deal with landing the fish.
If they are small, just lift them out of the water with the line and rod. If you catch a 3 pound bass or larger, you can't "flip" them on shore with that light of gear. You'll have to hold the rod in one hand, lifting the fish's head slightly out of the water, while you use the other hand to grab the fish. If it's a bass, crappie, bluegill, or catfish, you can put your fingers in it's mouth and "lip" it.
Catfish have slightly sharper teeth than bass, but use your man hands and it is okay. Catfish also have a single spike on either side and on the back. They will thrash around and jab you with them. It sucks, don't let that happen. Put the cat on the ground, put your hand right behind the fin on the back and press him into the ground lightly to control him while you unhook him.
Never go without needle nose pliers. Walmart cheapo pliers are sufficient.
For bass, bluegill, crappie, don't put them on the ground if you can avoid it, it's bad for them. Grab them by the body or by the lip.
Take your picture and throw them back.
No longer than 2 minutes out of water, any more than 5 and they start dying.
You need a fishing license, kids under 16 do not.