Lauren, it is easy once you get the hang of it.
For starters, adding those pH up and down solutions is bad for your animals. Having a less-than-ideal pH is better than wild swings in pH.
Second, there's no need to change 100% of the water at any time.
What size tank do you have?
I'll just kind of add on to what Ed has said. Your axolotl excretes ammonia. You need a special bacteria in your tank that will convert ammonia to nitrites. Nitrites are still poisonous, so you need a second kind of bacteria to convert nitrites to nitrates.
You can't get these bacteria from a bottle (unless you get refrigerated bio-spira, but most stores do not carry this). You need to grow the bacteria over time. It usually takes between 1 and 3 months.
The bacteria will live on the solid surfaces in the tank. They'll grow in the substrate (the sand/rocks that you use as a floor covering), they'll grow especially in the filter, and on any decorations.
The easiest way to cycle your aquarium would be to take the axolotls out and put them in a temporary holding bin (I'm a BIG fan of the plastic storage tubs by rubbermaid!). Keep the bin as simple as possible. Just a few decorations, places to hide, no filter. You'll need to change the water in this bin nearly daily.
As for the permenant tank: Keep the filter running. Get test kits for ammonia, nitrite, and nitrate. Add axolotl poo that you remove from the holding bin as a food for your bacteria. Test the water frequently. You should see ammonia levels start to rise. Then as the ammonia levels drop, your nitrite levels should rise. Then both ammonia and nitrite levels will drop and nitrates go up. Once you have a 0ppm reading for ammonia and nitrite, do a 30% water change to reduce the levels of nitrates, and you've got a cycled tank. Then you need to change about 10% of the water once a week to keep it maintained. I recommend weekly testing midway between water changes, so you know what is 'normal' for your tank.