Answer 1

You walk up to a cuttable tree (they're small and fragile-looking), click the A button, and click YES, when the choice box pops up.

Answer 2

First teach the Hm to a pokemon that knows it, then stand near a tree, and press A, it will ask if you want to cut it. just say yes, and the pokemon will cut it down for you.

Answer 3

You stand in front in a tree and press "a" and it says this is an odd tree want to cut it down so press "a" again and you will cut it down. In a battle just press "a".

Answer 4

My answer is the same as all those before me. However, I jsut want to add that in Gen 1, you actually had to select Cut from the Pokemon Menu Screen.