Here are the basics -
1) 2 foot tank minimum - don't buy a small tank with the intent to upgrade. Always buy for the adult size - it will save you a ton of $ in the end, and releave them from a ton of stress and possible illness from being cramped.
2) keep it cold! under 72*F as a max! 75*F + can lead to illness and death.
3) no gravel - they are known substrate eaters because they gulp food down - keep it bare or a VERY fine sand (bare can be safer while they are younger)
4) provide hiding spots - even sideways flower pots work great
5) food - - keep it simple and make it the best = earth worms. Cut up when young, whole when they are adults. It is the very best diet you can have them on.
6) no fish or snails in the tank. They will eat them and can choke to death on them.
7) filtrate - the frills on the side of their head are actually gills. Like a fish, they are very sensitive to their environment.
3) do not over crowd and do not house young axolotls together (under 4" and you risk them nibbling on each other). A two foot tank minimum for one adult, add a foot of tank length per axie.