What is an HM.
HM 1 - Cut. To find Cut, you must be at least to Vermillion City. In Vermillion City, go to the S.S. Anne in the southern part of the city. When you have gone through the ship for a while, you will find Gary. Behind Gary is the stairway to the Captains room.If you help him get over his seasickness, he will give you HM 1.
HM 2 - Fly. To find Fly, you must be at least to Celadon City and have one Pokémon with cut in your group. Fly is very useful, because it lets you fly to any town you've already been too on any "Flying" or "Bird" type Pokémon. Go to the Biking Road entrance, in the far left of Celadon City. Slightly before the Snorlax, you will find a bush. Cut down this bush to find a small field. Go to the left and enter the building directly above the Biking Road entrance. Go out of this building from the other side. You will find another small field with a house in it. In the house is a girl. She will give you HM 2.
HM 3 - Surf. Surf is in the Safari Zone. You must go to the right, to the top of that large field, to the left, to the top of that field, to the left again, and down. You should now be in a place with an item ball in it. That has the Warden's Gold Teeth. Now go to the left. There is a small building (the Secret House). The man inside of the Secret House will give you HM 3.
HM 4 - Strength. To find Strength, do the same thing as you did with Surf. All you need are the Gold Teeth. Take the Gold Teeth to the Warden's house (to the right of the Pokémon Center and to the left of the Fishing Guru's Brother's house). Talk to the Warden and he will give you Strength. Teach it to one of your Pokémon and have them move the boulder in his house. You will find a Rare Candy there.
HM 5 - Flash. Flash is in the Viridian Forest. You need Cut to find Flash. The easiest way to find HM 5 is to take Diglett's Cave from Vermillion City to Viridian Forest. When you exit the Cave, you will find a house directly below the exit. Inside of the house is a girl who will give you a Mr. Mime for an Abra. Continue below from this house to find a place where you must use cut. Continue on and you will find, among other things, item balls with a Moon Stone and a Rare Candy (both are very useful). Before you find the Moon Stone, however, you will find a large building. Inside this building there are two people. One of them is Professor Oak's Aid. He will give you HM 5 if you have caught (or evolved) at least 10 Pokémon.