Silver first appears in the Generation IIgames, lurking outside of Professor Elm's lab, looking through the window. When talked to, he will deny everything and push the player away. During the player's journey to Mr. Pokémon's house, Silver makes his move, stealing one of Elm's two remaining starter Pokémon (coincidentally always the one that is strong against the player's choice). He will meet with the player on the outskirts of Cherrygrove City, battling to get through. A policeman will later ask for the name of the rival, and the rival will be called the name the player gives for the rest of the game.
Silver shows a strong dislike of Team Rocket. He considers them to be weak, and vows to take them, as well as any other weak Trainer, down. He steals an unnamed Pokémon from a Trainer in Cianwood City and while Ethan/Kris/Lyra attempts to take down Team Rocket in Mahogany Town and Goldenrod City, he interferes to prove himself. It is in the Mahogany hideout that he meets with Lance, Champion of the Elite Four at Indigo Plateau. Silver challenges Lance and is easily defeated by the dragon Trainer, who then proceeds to berate Silver for his callous ways towards training Pokémon. Though Silver is outraged for losing to someone with such an attitude, the loss and Lance's words ultimately set him on the path to becoming a better person. In HeartGold and SoulSilver, when Team Rocket takes over the Goldenrod Radio Tower, Silver first blows the player's Team Rocket disguise, unaware of the player's plan to sneak in by pretending to be a member of Team Rocket. He later follows the player to the Goldenrod underground and they battle Team Rocket, hoping that Lance will reappear and he can request a rematch.
By the time the player reaches Victory Road, Silver battles against the player not out of malice, but to prove that he is a good Trainer. He is defeated and departs to continue training. The player battles Silver on Mt. Moon, and though he loses he claims he can feel his Pokémon getting stronger, and resolves to train at Dragon's Den.
After the player has become Champion, Silver can indeed be found training in the Dragon's Den on Tuesday and Thursday, where he cannot be battled. On Monday and Wednesday, he will appear at Indigo Plateau and will challenge the player to a battle if they appear there. He does not appear at all on Friday or the weekends, indicating that he may in fact take the day off, resting his Pokémon. When battled this seventh and final time at Indigo Plateau, Silver seems to have finally learned to care for his Pokémon properly, as his Golbat has evolved to Crobat, which only occurs when Golbat is very friendly. This is further expressed in Generation IV when his starter Pokémon starts to follow him around, much like the player's Pokémon; Professor Elm even expressly states that Silver's Pokémon have come to trust him when Silver returns to the lab, presumably to return the starter he stole. In Pokémon HeartGold and SoulSilver, Lance and Clair will appear in the Dragon's Den and challenge the player and Silver to a Multi Battle following the battle at Mt. Moon giving him the chance to avenge his loss from earlier.
In terms of personality, Silver is initially the darkest of the rivals in the series. While most other rivals are generally good-natured, or at least zestful enough to crack a joke at the player, Silver is (at first) cruel, hateful, power-obsessed, and even physically abusive, pushing the player character around several times. Even after he starts to become kinder, he remains a rather serious individual. He does, however, express genuine happiness when Elm allows him to keep the Pokémon he stole.
The starter Pokémon that Silver has will depend on which Pokémon the player chose to bring on Professor Elm's errand at the beginning of the game. As with most rivals, it will be the Pokémon whose type weakens that of the player's starter.