So you're interested in owning axolotls. Great! They are fantastic pets. However, it's important you know what you're getting into before buying an animal...
Nitrogen Cycle
Before we get into any care requirements, it's important we talk about the nitrogen cycle and how to cycle your tank. In an aquarium, your axolotl will produce waste. This waste is turned into ammonia. Ammonia is TOXIC to axolotls. It can very easily give them ammonia burns and even kill them. Because of this, axolotls need to live in a tank that is cycled. A cycled tank will have beneficial bacteria in it that will turn the ammonia into nitrites, which it then turns into nitrates. Beneficial bacteria takes time to grow in an aquarium. It will not happen overnight. It can take weeks to MONTHS to cycle a tank.
Now, you may be asking how to cycle an aquarium. There are two ways.
The first way is called fish in cycling. This is where you have your aquatic creatures in the tank as you cycle. This is not reccommended with ANY creatures, but even moreso not recommended with axolotls due to the stress and danger it causes. Please do not cycle your tank with your axolotls in it! It could cause your axolotl to develop ammonia burns, or even kill it.
The second way to cycle your aquarium is fishless cycling. Fishless cycling is the only way you should cycle your tank for axolotls. The way you fishless cycle a tank is by adding pure ammonia into the water daily. Your beneficial bacteria should start turning your ammonia into nitrites, and then into nitrates. Dose up to 2ppm ammonia until your tank can turn 2ppm ammonia into 0ppm ammonia and 0ppm nitrite in 24 hours. You can use this by using pure household ammonia or store bought aquarium ammonia like Dr. Tim's Ammonia. Either will work.
You can help speed up your cycle by adding in filter media from another tank that is already cycled. The bottled beneficial bacteria is usually a waste of money, however, I have heard good things about Fritz Fishless Fuel.
Water Parameters
To test your water parameters, you will need a liquid test kit. The only test kit I recommend is the API Master Test Kit. Do not buy the strips, as they are very innaccurate. At the end of the cycle, your parameters should look somewhat like this regarding the ammonia, nitrites, and nitrates. Its normal to have very high nitrates at the end of a cycle, and its recommended to do daily partial water changes on the tank and dose up to 1ppm of ammonia until your nitrate is at 5-10ppm. When your tank is cycled and ready for an axolotl, your ammonia should read 0ppm, your nitrite should read 0 ppm, your nitrate should read 5-10ppm, and your pH should be between 6.5-8.
Axolotls should be kept at a temperature of 60-68F. Anything higher can be dangerous and stress them out. Because of this, you should not have a heater in your tank. 99% of the time, your tank will be too warm, and you will need a chiller or fan to keep the temperature down.
Tank Size
The absolute minimum tank size per axolotl is 29 gallons. This is because of the amount of waste they produce. A larger filter will not let you keep your axolotl in anything smaller than 29 gallons. This is because the nitrates get too high to be safe. Your nitrates should be 5ppm-20ppm. At 20ppm, its time for a water change. I do water changes on my tanks weekly. On a tank like a 20 gallon long, you will need to be doing water changes every 2-3 days. This can stress your axolotl out a lot. While 29 gallons is the minimum size, bigger is ALWAYS better, and 40 gallons is a better tank size for an axolotl. For two axolotls, you will want to aim for 60-75 gallons. For 3, 90-110 gallons, and so on. Because of this, I will not adopt out my axolotls to people unless they have a 29 gallon tank or bigger that the axolotl will be living in. If your tank is still cycling, or your cycle crashes, you can always tub your axolotl, however having a tank cycled before you buy your axolotl is always advisable as tubbing can be stressful on axolotls.
Feeding & Diet
The most nutritious food for axolotls are live earthworms. All the babies that I sell are already transitioned into cut up red wigglers for the convieniance of the new owner. Variety is important as well though, and some other acceptable foods to feed occassionally are blackworms, pellets, brine shrimp, and bloodworms as a treat. Their main food should be earthworms, though.
Substrate
Substrate is a widely debated topic in the axolotl community. The safest substrate you can have is no substrate at all, however, this does not always look aesthetically pleasing. Slate and untreated tile are two other safe substrates, however, they must be siliconed down to prevent debris getting trapped underneath and causing an ammonia spike. Sand with grain sizes under 1mm is only safe for axolotls over 6 inches. Anything over 1mm is dangerous and can cause impaction. Some safe sands are Caribsea and Exoterra Riverbed sand. Home Depot childrens play sand, gravel, and planting substrate are NOT suitable for axolotls, despite people using it often. All are impaction risks.
Tankmates
Tankmates are another widely debated topic. The only truly safe tankmates for your axolotls are shrimp, however they may get eaten. Fish cannot live with axolotls. This includes feeder fish, especially goldfish and other fish that contain thiaminaise. Feeding your axolotls any kind of fish is not recommended, as they offer nothing crucial nutritionally that earthworms don't and the bones can be hard to digest. Other axolotls can pose a risk to your axolotl as well. They are solitary creatures and don't benefit from having other axolotls in the tank. This isn't to say that they can't live with other axolotls. It can be done. However, you should be 100% certain of the axolotls sexes before you cohab any axolotls. Otherwise, you may run into trouble with breeding. Males will overbreed the females if they are not separated, so they should be separated immediately and all eggs frozen. Raising axolotl eggs is hard work, and any axolotls bred should have well documented lineage and be as distantly related as possible to avoid genetic defects.