Eevee can be found in a building in Celadon City, where you can also buy a Water Stone for 2100 Pokédollars. If you’re low on money, there is also a Water Stone in the Seafoam Islands.
As one of three evolutions of the obligatory Eevee (unless you got something from the Game Corner), Vaporeon is very easy to obtain. It may seem like it is outclassed by other Water-types, like Blastoise, Tentacruel, Lapras, or Gyarados, but in reality it is something so much more. It is one of the bulkiest Pokémon in the game, with 130 HP, and it's also relatively powerful with 110 Special Attack. No one would ever call Vaporeon's movepool wide, but it has just enough to function with. Unfortunately, after getting it, it suffers from having to sit out against the next gym leader. It does make Blaine and Giovanni cakewalks, but honestly any Water-type does the same. It can also be taught Ice Beam to defeat Lance's Dragons, but again, any Water-type does the same. Why use Vaporeon, exactly? Well, for one, it has some of the most balanced stats for a Water-type in-game, being useful with every stat except Speed and Attack. It also has superb HP and comes at a decent level, and is more powerful than its main rivals, Blastoise and Lapras. Basically, if you immediately need a Water-type and would rather not waste your time with a Magikarp and you want something more powerful than Lapras, by all means use Vaporeon.
Gym #3 - Lt. Surge (Vermilion City, Electric-type): First, why did you delay fighting Surge so long? Second, no, because Vaporeon is weak to Surge's Pokémon and can only really hold its own if it carries Surf. Even then, stay FAR AWAY from this.
Giovanni (Rocket Hideout, Ground-type): Vaporeon can defeat Onix and Rhyhorn without any problem whatsoever. Kangaskhan, however, is a different story. It will probably live through a Surf, and Mega Punch will do a ton of damage to Vaporeon. Also, Kangaskhan WILL be going first. It's probably not a good idea.
Gym #4 - Erika (Celadon City, Grass-type): Yeah, no. Vaporeon might be able to take this Gym on if it knows Ice Beam for some strange reason, but seriously, what are you doing to yourself? You will most likely have a Flying-type or ANYTHING better to take her on. Don't use Vaporeon.
Gym #5 - Koga (Fuchsia City, Poison-type): While the Koffings will go down in one hit, Weezing will likely take at least two and Muk will be tanky enough to take more than that. Muk will also ruin Vaporeon's day with Minimize and poison, which will cripple Vaporeon. Use something else for Muk, or pack your X Accuracy and Full Heals.
Fighting Dojo (Saffron City, Fighting-type): Vaporeon's probably not the best choice here. Everything (except Hitmonchan) will be hitting very hard on the physical side, which will likely 2HKO Vaporeon. While Vaporeon might be doing a lot of damage with STAB Surf, leave that only for the slow Machop family and the weak Hitmonchan. Primeape and Hitmonlee are too fast and strong for Vaporeon to take on by itself.
Gym #6 - Sabrina (Saffron City, Psychic-type): Actually, Vaporeon's a pretty good Pokémon here. Its good Special bulk allows it to take STAB Psychics pretty well, and Surf will be hitting pretty hard as well, if not harder than it was being hit by Psychic. Bite is also an option here, but it should only be used against the Slowpokes and Slowbros because STAB Surf does more than super-effective Bite.
Rival (Silph Co.): Vaporeon laughs at whatever Fire-type he has, so by all means use it here. Pidgeot isn't very powerful or bulky, so Vaporeon's pretty good here too. Gyarados and Blastoise are a bit too bulky to be taken down by Vaporeon, but you can choose to painstakingly take them down with Toxic. Alakazam only has Future Sight as an attacking move, so use Vaporeon all you want here. Exeggcute will go down to a Bite or two since it's really weak, but if you chose Squirtle, keep it away from Venusaur.
Giovanni (Silph Co., Ground-type): Pretty much the same things here. Vaporeon also handles Nidoqueen quite nicely.
Gym #7 - Blaine (Cinnabar Island, Fire-type): LOL.
Gym #8 - Giovanni (Viridian City, Ground-type): Everything is drowned by Surf about as easily as Blaine was. Go for it.
Rival (Route 22, pre-Elite Four): Same as before, except now he has a Rhyhorn. Take a guess as to how hard it is for Vaporeon to handle that. Just guess.
Elite Four Lorelei (Indigo Plateau, Ice-type): Unless you really want to handle Jynx and Slowbro using Surf and Bite, respectively, it's probably better to use an Electric- or Grass-type here. Vaporeon can't even really Toxic-stall here: Dewgong has Rest and Safeguard, Lapras has Confuse Ray, Jynx is faster and has Lovely Kiss and Attract (ignore if Vaporeon is female, which it probably isn't), and Cloyster just loves to not get hit. However, feel free to Toxic-stall the Slowbro.
Elite Four Bruno (Indigo Plateau, Fighting-type): Both Onix are killed in seconds. His Fighting-types, again, are probably too strong Physically for Vaporeon to be taking on. Well, maybe not Machamp because it's slow, but Hitmonlee is definitely a threat.
Elite Four Agatha (Indigo Plateau, Poison-type): Her first Gengar has Toxic - bad, bad. Her second one has Hypnosis and Nightmare, so it'll basically be out-stalling you. Haunter will probably kill itself with Curse, so go right ahead. Golbat can be handled with Ice Beam, and Arbok will probably be 2HKO'd by Surf, but watch out for Sludge Bomb because it'll hurt.
Elite Four Lance (Indigo Plateau, Dragon-type): Bar none, Vaporeon's time to shine in the E4. Literally everything is easily handled by Vaporeon. It is fully capable of OHKOing his three Dragons with Ice Beam, and Aerodactyl is defeated by Surf. Gyarados is the only really weird thing, but Toxic-stall beats it.
Champion Rival (Indigo Plateau): Fire-type is the same as before, and Vaporeon handles Pidgeot better than ever now because of Ice Beam. Alakazam is similarly handled, but Vaporeon should now stay away from Exeggutor/Venusaur even if you have Ice Beam. Rhydon... well, is Rhydon, and Blastoise/Gyarados can be Toxic-stalled but be careful, because Gyarados is capable of boosting itself to levels that overwhelm Vaporeon.
Post-Game Vaporeon is pretty decent against Mewtwo, thanks to its majestic bulk. You will still need patience and heals to wear it down, though.
Vaporeon starts off with Eevee's terrible moveset: Tackle, Tail Whip, Sand-Attack, Growl. Gross. At level 23 Vaporeon gets Quick Attack, which is good for finishing off weakened foes. 7 levels later, you get Bite, which isn't great but is better than its other moves. At level 36 you get Aurora Beam, which is good for the time being but should be replaced by Ice Beam once you get that. Haze comes next and is interesting, but since very few opponents actually set up, it's rather situational. Acid Armor comes 5 levels later, and it's another situational move that patches up its lackluster defense. Its final level-up move, Hydro Pump, should definitely be considered, but its shaky accuracy makes it a gamble. It's a good idea to have it as a last resort alongside Surf.
As for TM's and HM's, Vaporeon gets Water Pulse, if you still have it. It should replace Tackle. Once you get the Surf HM, that is a move which should NEVER leave Vaporeon's moveset because it is its most reliable move. Roar is an option, but it's also rather situational because opponents rarely set up. Besides, you're better off with Haze in that regard. Hail and Sunny Day should not even be worth considering. Rain Dance is always fun, as it boosts Vaporeon's STAB, but is probably not going to be too helpful. Toxic is a fun option which allows Vaporeon to stall out opponents. Hidden Power is only good if it gets a decent type. Oh, and it HAS to be Special. Only go for it if it's Grass or Electric, honestly. Don't even consider physical moves; they're worthless. Rest, Attract, Substitute, Double Team, and Protect are options too. Mimic is also rather worthless for obvious reasons. The cream of the crop is Ice Beam, which you should get by money grinding and serves as Vaporeon's best coverage move. Blizzard's always an option if Ice Beam's too expensive for you (which it shouldn’t be, since you can literally get all the money you want through use of the Vs. Seeker).
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
What Nature do I want? You want Modest. That is THE nature for it. If you can't get that, definitely go for any -Attack nature. Bold and Calm are better than Timid, but that works too. -Special Attack natures are pretty terrible, truth be told.
At what point in the game should I be evolved? As soon as you get it. Come on, the stone is in the same town!
How good is Vaporeon in a Nuzlocke? Honestly, it's pretty great. It's bulky, powerful, and it has enough of a movepool to work with. It's definitely THE Eeveelution of choice.