Axe

Axes are a type of tool that can chop down trees when stood next to and facing them. The regular axe is the easiest axe to obtain, by going to Tom Nook's Store while the other two, the silver and gold axe, are harder to obtain. After a regular axe is used against something 50 times, the axe will shatter. This will be apparent when the image of the axe in the inventory appears to have a crack in the blade. However, Silver and Golden Axes do not break and can chop down trees faster than normal axes. They can all be used on money rocks as a substitute to the regular shovel.

Regular
Purchase from Tom Nook's Store for 400 Bells.

Gold
Farley will give you a golden axe.

Regular
Purchase from Tom Nook's Store for 400 Bells.

Gold
Complete the Golden Axe Trading Event.

Regular
Purchase from Tom Nook's Store for 400 Bells.

Silver
Throw an axe into the town fountain (obtained through donation to the Town Fund). Once thrown in, sweet-talk Serena in hopes of getting one, only one try per day.

Gold
The same way you get the silver axe, but appears much more rarely.