Hi Jason,
Cycling in a nutshell is establishing beneficial bacteria that breaks down toxins such as ammonia into a non toxic form.
This article explains it in detail:
http://www.caudata.org/cc/articles/cyclingEDK.shtml
Cycling takes anywhere from one to three months to complete. While your axie is living in the water, you will need to do 20% daily partial water changes.
If you haven't already, I would recommend you purchase test tube test kits for Ammonia, Nitrite and Nitrate. The readings for Ammonia and Nitrite should read as '0' - any reading higher than this is toxic to an axolotl - this is why 20% daily water changes are necessary as they keep these levels under control while the tank is cycling. When Ammonia and Nitrite read at a consistant '0' and the Nitrate reading reads from 10-60 - this indicates the cycle is complete and water changes need only be done once a week at this point.
Water cloudiness can be also caused by accumulated grot in the water such as excess food and poop. Do you spot clean after the axie by removing poop and left over food each day? Axies are right messy little creatures, it is necessary to be diligent with spot cleans. Do you have a Turkey Baster? These are an essential tool in an axie keepers arsonal in the fight against grot!
A gravel syphon is good for this purpose as well.
What sort of substrate do you have? If you have large stones then the grot will sift under these and the only way to clean it out is to shift those rocks.
If you have sand, was it cleaned thoroughly before adding to the tank?
What sort of filter do you have? If it is an undergravel filter, this may be the cause of the cloudiness as grot gets trapped under the substrate and the filter and never leaves the water.
If you feed your axies on pellets, any leftovers from feeding can also cloud the water up if not removed.
