Below are the names and locations of all 50 TMs found in Pokémon Gold & Silver. Please remember that unlike modern Pokémon games they are only usable once.

TM01 Dynamicpunch Defeat Cianwood Gym
TM02 Headbutt Ilex Forest or Goldenrod Dept. Store (¥2000)
TM03 Curse Celadon Mansion at night—Speak to the man on the roof
TM04 Rollout Route 35
TM05 Roar Route 32
TM06 Toxic Defeat Fuschia Gym
TM07 Zap Cannon Recover Machine Part in the Power Plant (near Route 10)
TM08 Rock Smash Route 36 or Goldenrod Dept. Store (¥1000)
TM09 Psych Up Traded Abras/Kadabras from Generation I (R/B/Y)
TM10 Hidden Power Lake of Rage or Celadon Dept. Store (¥3000)
TM11 Sunny Day Goldenrod Radio Tower (after defeating Team Rocket) or  Celadon Dept. Store (¥2000)
TM12 Sweet Scent Building between Route 34 & Ilex Forest
TM13 Snore Route 39—Feed sick Miltank berries, or Dark Cave
TM14 Blizzard Goldenrod Game Corner (5500 coins)
TM15 Hyper Beam Celadon Game Corner (7500 coins)
TM16 Icy wind Defeat Mahogony Gym
TM17 Protect Celadon Dept. Store (¥3000)
TM18 Rain Dance Slowpoke Well or Celadon Dept. Store (¥2000)
TM19 Giga drain Defeat Celadon Gym
TM20 Endure Burned Tower in Ecruteak City
TM21 Frustration Goldenrod Dept. Store—Available on Sundays if a Pokémon dislikes you (5F)
TM22 Solar beam Route 27
TM23 Iron tail Defeat Olivine Gym
TM24 Dragons breath Defeat Blackthorn Gym
TM25 Thunder Goldenrod Game Corner (5500  coins)
TM26 Earthquake Victory Road
TM27 Return Goldenrod Dept. Store—Available on Sundays if a Pokémon likes you (5F)
TM28 Dig National Park
TM29 Psychic Saffron City—Mr. Psychic’s House or
Celadon Game Corner (3500 coins)
TM30 Shadowball Defeat Ecruteak Gym
TM31 Mud-slap Defeat Violet Gym
TM32 Double Team Celadon Game Corner (1500 coins)
TM33 Ice punch Goldenrod Dept. Store (¥3000)
TM34 Swagger Olivine Lighthouse
TM35 Sleeptalk Goldenrod Dept. Store Basement
TM36 SludgeBomb Route 43
TM37 Sandstorm Near Tohjo Falls on Route 27—Must show woman inside house lead Pokémon with high Friendship level or Celadon Dept. Store (¥2000)
TM38 Fire blast Goldenrod Game Corner (5500 coins)
TM39 Swift Union Cave
TM40 Defense Curl Mt. Mortar
TM41 Thunderpunch Goldenrod Dept. Store (¥3000)
TM42 Dream Eater Viridian City—Receive from man in southwestern part of city, requires Surf or Cut
TM43 Detect Lake of Rage or held by Nidoran♀/Nidoran♂ when traded from Generation I (R/B/Y)
TM44 Rest Ice Path
TM45 Attract Defeat Goldenrod Gym
TM46 Thief Team Rocket’s Hideout in Mahogony Town (B2F)
TM47 Steel Wing Route 28 or Rock Tunnel
TM48 Fire punch Goldenrod Dept. Store (¥3000)
TM49 Fury Cutter Defeat Azalea Gym
TM50 Nightmare Route 31—Deliver Randy’s Spearow

Pokémon Gold & Silver also have 7 HMs, or Hidden Machines, which are not only attacks, but also allow you to better traverse Johto and Kanto. These can be used multiple times, but cannot be un-leared without the help of a Move Deleter.

HM01 Cut Ilex Forest (Requires Hive Badge to use outside of battle)
HM02 Fly Cianwood City (Requires Storm Badge to use outside of battle)
HM03 Surf Defeat Kimono Girls in Ecruteak City (Requires Fog Badge to use outside of battle)
HM04 Strength Olivine City (Requires Plain Badge to use outside of battle)
HM05 Flash Sprout Tower in Violet City (Requires Zephyr Badge to use outside of battle)
HM06 Whirlpool Rocket Hideout in Mahogony Town (Requires Glacier Badge to use outside of battle)
HM07 Waterfall Ice Path (Requires Rising Badge to use outside of battle)