The Move Tutor appears in front of the Goldenrod City Game Corner every Wednesday and Saturday, after you've beaten Red (Ash) in Mt. Silver. For 4000 coins (you'll need to bring your Coin Case to pay), the Move Tutor will teach one of your Pokemon either Thunderbolt, Flamethrower, or Ice Beam. Following is the Pokemon that can learn each move.
Flamethrower (CM01*)
Charmander, Charmeleon, Charizard, Nidoqueen, Nidoking, Clefairy, Clefable, Vulpix, Ninetales, Jigglypuff, Wigglytuff, Growlithe, Arcanine, Machop, Machoke, Machamp, Geodude, Graveler, Golem, Ponyta, Rapidash, Slowpoke, Slowbro, Grimer, Muk, Cubone, Marowak, Lickitung, Koffing, Weezing, Rhyhorn, Rhydon, Chansey, Kangaskhan, Magmar, Tauros, Gyarados, Flareon, Aerodactyl, Snorlax, Moltres, Dratini, Dragonair, Dragonite, Mewtwo, Mew, Cyndaquil, Quilava, Typhlosion, Cleffa, Igglybuff, Togepi, Togetic, Slowking, Dunsparce, Slugma, Magcargo, Remoraid, Octillery, Houndour, Houndoom, Magby, Blissey, Entei, Tyranitar, Ho-oh
Thunderbolt (CM02)
Raticate, Pikachu, Raichu, Nidoran (f), Nidorina, Nidoqueen, Nidoran (m), Nidorino, Nidoking, Clefairy, Clefable, Jigglypuff, Wigglytuff, Meowth, Persian, Mankey, Primeape, Magnemite, Magneton, Grimer, Muk, Gastly, Haunter, Gengar, Voltorb, Electrode, Lickitung, Koffing, Weezing, Rhyhorn, Rhydon, Chansey, Kangaskhan, Staryu, Starmie, Mr.Mime, Electabuzz, Tauros, Gyarados, Lapras, Jolteon, Porygon, Snorlax, Zapdos, Dratini, Dragonair, Dragonite, Mewtwo, Mew, Chinchou, Lanturn, Pichu, Mareep, Flaaffy, Ampharos, Aipom, Misdreavus, Girafarig, Dunsparce, Snubbull, Granbull, Porygon2, Elekid, Miltank, Blissey, Raikou, Tyranitar, Lugia, Ho-oh
Ice Beam (CM03)
Squirtle, Wartortle, Blastoise, Raticate, Nidorina, Nidoqueen, Nidorino, Nidoking, Clefairy, Clefable, Jigglypuff, Wigglytuff, Psyduck, Golduck, Poliwag, Poliwhirl, Poliwrath, Tentacool, Tentacruel, Slowpoke, Slowbro, Seel, Dewgong, Shellder, Cloyster, Krabby, Kingler, Cubone, Marowak, Lickitung, Rhyhorn, Rhydon, Chansey, Kangaskhan, Horsea, Seadra, Goldeen, Seaking, Staryu, Starmie, Jynx, Tauros, Gyarados, Lapras, Vaporeon, Porygon, Omanyte, Omastar, Kabuto, Kabutops, Snorlax, Articuno, Dratini, Dragonair, Dragonite, Mewtwo, Mew, Totodile, Croconaw, Feraligatr, Chinchou, Lanturn, Marill, Azumarill, Politoed, Wooper, Quagsire, Slowking, Qwilfish, Sneasel, Swinub, Piloswine, Corsola, Remoraid, Octillery, Delibird, Mantine, Kingdra, Porygon2, Smoochum, Miltank, Blissey, Suicune, Tyranitar, Lugia
The Move Tutor can teach Pokemon only once a day.