You are finally given control over yourself. You can interact with several things in this room and almost every room from here on out. These include the SNES in front of you, among many others, though these are usually just for continuity and entertainment, and as such will only be mentioned when they have a direct effect upon the game. For starters, walk up to the PC in the top left of your room and open up the item storage to withdraw a potion. Now, head downstairs. You mom is sitting at the table and mentions she knew the day would come when you would leave the house. Head out and try to walk north into the grass to be stopped by Professor Oak, as he comes to warn you of the dangers of travelling alone.
If you're playing Yellow Version, you are ambushed by a wild Pikachu, but Professor Oak catches it. You follow him back to his lab where you are presented with a pokeball, which contains your very first pokemon! In Red and Blue, you will get to choose between three starters on the table: Bulbasaur, the grass type, Charmander, the fire type, and Squirtle, the water type. Whichever you choose, Blue will choose the Pokemon that yours is weak to. In Yellow, before you can take the only pokemon on the table, Blue comes to take it first. As a consolation, Professor Oak decides to give you the wild Pikachu he just caught, with the warning that it may misbehave until you have tamed it.
NOTE: Now is the best chance to abuse the happiness glitch present in Yellow.
If you're on Red or Blue Version, Blue will fight you with the pokemon you're weak to: Bulbasaur, if you chose Squirtle; Charmander, if you chose Bulbasaur; or Squirtle, if you chose Charmander. For now, neither of these pokemon has learned any elemental moves, so the weakness shouldn't factor in. Whichever your pokemon, it'll have one physical damaging move, Tackle or Scratch, and one status affecting move, Tail Whip or Growl. There's no real applicable benefit to the status changing moves at this point in the game, so your basic strategy is to attack mercilessly until you've won. Barring any critical hits on your rival's side, you should win. If Blue happens to use nothing but his one damaging move, too, you may be in danger of losing, in which case you should use the Potion you grabbed from the PC before leaving your room.
• Red/Blue: Rival Battle
If you're playing yellow, after you have gotten your Pikachu, Blue will challenge you. You have two moves, Thundershock and Growl, and the key to winning this fight is using your Thundershock. There are a few things that can happen here. Eevee can use Tail Whip, which will lower your defense, but since it wastes a turn which will do extra damage in order to enable the extra damage, this effectively does nothing in such a short battle. Eevee can also use tackle, which is slightly more damaging than your Thundershock now. If Eevee uses nothing but tackle, you're going to lose unless you use the Potion we grabbed from the computer earlier. There's also a chance that either attack will be a critical hit, in which case the hit pokemon will take much more damage than normal, as well as either pokemon's attack can miss. And there's a slight possibility that Thundershocking Eevee will paralyze it. Overall, you're all but guaranteed a win if you use nothing but Thundershock and use the Potion if Pikachu's health drops too low.
• Yellow: Rival Battle
After the battle, given a win, your Pokemon should level up. Back in Professor Oak's lab, Blue leaves in defeat. On Yellow, Pikachu emerges from his pokeball on his own. Professor Oak realizes that Pikachu dislikes pokeballs, and encourages you to let it walk with you to increase it's happiness. At present it should have moderate happiness with you, indicated by a neutral face if you interact with it. If your Pikachu needs health, you can visit Mom for a free healing. When you're ready, head north to Route 1.