Adult Tropical Hobbyist with a Single Tank.
One of the most common situations. Snoop around a little to see what equipment they have. Equipment they might need:
-pH/ammonia/nitrite test kits. These save fish lives, but too many people don’t buy them.
-spare heater
-fluorescent light bulb of correct size and shape. These do burn out.
-fluorescent light hood. Vastly better than incandescent.
-filter inserts for their particular filter
-frozen fish food
-aquarium salt. Useful medication for several diseases, and really cheap. Also good for a few species to have permenantly in their water.
-aquarium thermometer. Essential and extremely cheap.
-hospital/quarantine tank. 5 gal tank with heater and mechanical filter. It is really, really useful to be able to quarantine sick or newly acquired fish. Second hand tanks are a good way to find these cheap.
-general aquarium book

Child with A Single Small Unheated Aquarium
-fish tank decorations. Many children adore these and they are really easy to find in any petstore. They are often among the cheapest fishtank related gifts.
-a ten gallon kit. If the child shows real interest in their aquarium, get them decent equipment. A lot of the little plastic kits are nearly junk. If a plastick kit has goldfish in them, goldfish that live more than a year or so will outgrow the tank.
-a small filter. Many of these tanks don’t come with them and it really improves tank conditions and the ease of keeping fish.
-LED tank light. Looks pretty, uses little energy and now you can grow low-light live plants.

Adult with Single Cold Water Tank
-pH/ammonia/nitrite test kits. These save fish lives, but too many people don’t buy them.
-fluorescent light bulb of correct size and shape. These do burn out.
-fluorescent light hood. Vastly better than incandescent.
-filter inserts for their particular filter
-frozen fish food
-Aquarium salt. Useful for treatment of some diseases and very cheap.
-hospital/quarantine tank. 5 gal tank with mechanical filter. It is really, really useful to be able to quarantine sick or newly acquired fish. Second hand tanks are a good way to find these cheap.
-general aquarium book

One: Not do research. When I was first starting out, most of my problems stemmed from this.

Two: Not do regular partial water changes. Because I hadn’t done number one, I didn’t realize that I was supposed to do this, or how one should do this.

Three: Put too many fish in the aquarium. This compounded problem two.

Four: Assume fish are short lived. A few fish, like annual killifishes, live only a few months in nature but a Corydoras catfish can live for up to seven years in captivity and a goldfish can reach 20 years of age. If you make this wrong assumption, you may not notice you are doing something wrong.

Five: Buy one of each species. Many fishes are schooling and do not do as well without the company of their own kind.

Six: Keep goldfish in a goldfish bowl. Common goldfish can grow up to 12 inches in length and produce large amounts of waste. They do not belong in goldfish bowls.

Seven: Started with too small a fish tank. A five gallon tank makes a perfectly good aquarium, but water parameters can change quickly and you can’t keep many fish in there.

Eight: Not feed bottom feeders sinking food and depend on one brand of flake food for everything. Corydoras catfish get hungry and don’t feed off the surface. Fish benefit from a varied diet just as we do.

Nine: Keeping a Betta in a community tank without a plan B or enough hiding places for fish to get away. It killed one of my Neon Tetras, so we put the Betta in a breeding trap that wasn’t really big enough for it.

Ten: Put a Pygmy Gourami in with Cherry Shrimp. Pygmy Gouramis may have small mouths, but they regard shrimp as food and that one fish harassed the shrimp unmercifully. If it hadn’t been for the extremely thick live plants I think I would probably have lost all my Cherry Shrimp.

The last one wasn’t all that long ago, so such mistakes aren’t limited to beginners. No matter how much you think you know, do your research! And if you possibly can, keep a spare tank for quarentine, hospital use and unexpected animosities.