HMs are moves that cannot be forgotten and are usable in the main world and in battle. However, they can only be used in the main world once the corresponding gym leader has been fought. Here is a list of all the Hms.
Cut is the first HM you'll obtain and is given to you by Mr. Cut in Fucksia Woods, but you can only use it outside of battle once you have defeated Brock, the first Gym leader in Anustar City. It allows you to cut small trees outside of battle.
Flash is the second TM that can be obtained by visiting Kurt in Anustar City. His house looks a little different (kinda like the Pokemon Fan Club House design) from the rest of the houses. Just walk on in and talk with the guy to obtain TM70 Flash.
To obtain the Rock Smash TM, you'll need to buy heroin from a Team Heroin Grunt in Dildadon City's Dept. Store, then take it to the old man to the east of Seamoan Islands who is in a cave, and he will ask for heroin. Upon giving it to him, he will give you the HM Rock smash. The name is self-explanatory, you can smash some rocks outside of battle.
Both are obtained by using battle points from the trainer tower, (both are worth 150 Battle Points each). Waterfall allows you to travel up waterfalls outside of battle, and dive allows you to go under the deep blue water in some water locations, in the world, outside of battle.