You can use your axie and win battles in Origins daily in order for you to gain enough AXP to ascend your axies. Once your axie reaches a certain level and number of ascensions, you may even be able to upgrade their parts to have stronger cards. As long as the axie hasn't reached their daily AXP cap yet, your axies will get AXP from winning matches in Ranked mode.
Your axies will get varying amounts of AXP for each win from Ranked matches [with or without Stamina] in the Arena, depending on your rank.

The AXP you can gain from Origins is capped at [level of the axie * 1,500 AXP]. For example, a level 10 axie can earn a maximum of 15,000 AXP in Origins.
If your axie levels up while playing, it's Origins daily AXP cap automatically increases, allowing you to continue playing with that axie.
If your axie isn't gaining AXP even though it hasn't reached its Origins daily AXP cap yet, it's possible that the axie has already reached it's overall daily AXP cap which you can check on the axie's page in App.Axie.
You can also earn some AXP in Arcade Mode; albeit much lower compared to Ranked. But for players who want to relax and enjoy a more casual experience while still getting some much needed AXP, Arcade Mode could be a good option!

Players can assign up to 32 axies per land plot on Homeland, where their axies can earn AXP by doing various tasks. Each tasks gives a varying amount of AXP, with tasks that requires more effort/time giving more AXP.
The AXP each of your axies can gain on Homeland is capped at 10,000 AXP per day. Please check our Homeland AXP guide for more information on earning AXP in Homeland.
Axies can also gain AXP from winning matches in Axie Classic. Just like in Origins, each axie has a cap on how much AXP they can gain from Classic per day. The AXP you can gain from Classic is capped at 12,500 AXP per day for each axie, shared between Arena, Cursed Coliseum, and Grand Tournament.

You can get a maximum of 5,000 AXP from doing various activities with your axie in Project T, such as training them in the Dojo, farming with them, or taking them with you while catching butterflies in the Town Square.
Your axies can earn a maximum of 800 AXP per day in Raylights.
For your axies to start earning AXP, you need to meet the requirements: