Gold and Silver brought with it different ways to evolve Pokemon both old and new. Many of these would return in future generations and inspire even more lucrative methods.
Although stone-based evolution wasn't necessarily new, a new stone was indeed introduced in Gold and Silver. This would be the Sun Stone, which is only acquired by coming in first place at the Bug-Catching Content. The Sun Stone only seems to affect Grass-type Pokemon, one of whom is old and one of whom is new.
A secondary evolution stone was introduced in these games as well: the Everstone. It doesn't cause evolution though, it prevents it. It's useful for when you want to trade a Pokemon that evolves by trade. It, like the Sun Stone, is found by playing the Bug-Catching Content (though you have to come second).
This kind of evolution mainly affects Baby Pokemon, though it is also used for evolving Generation I Pokemon. To evolve using this method, the Pokemon must have very high happiness when it levels up. Sadly this means you can't evolve your Level 100 Golbat you brought in from Red or Blue with the Time Capsule, but it does mean you can theoretically have a Level 23 Crobat if you Golbat ingame.
Things that will jump start this process include levelling up the Pokemon, feeding it vitamins, giving it haircuts, and more. Click here for full details
This evolution method only affects one Pokemon: Eevee. It requires the same conditions to be satisfied as Happiness-based evolution, but the resulting Pokemon will be different based on whether it is morning and day or night.
Item trade-based evolution
One of the most common forms of evolution introduced was Item trade-based evolution. This method works the same way as trading with the exception being that the Pokemon must be holding an item to evolve. Trading via Time Capsule to older versions will not get you a Steelix in Red though, so keep that in mind. Often times the items you need only appear once in the overworld and are rarely found on wild Pokemon so don't make the decision lightly.
This is unique to Tyrogue. If, by Level 20, Attack is higher than Defense, you'll get Hitmonlee. If Defense is higher than Attack, you'll get Hitmonchan, and if both are equal, you'll get Hitmontop.
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