Evolve unlocks at league level 18 and it allows to trade a bunch of cards for a few of higher rarity. No gold is needed for this, but you need to have unlocked the higher rarity card to proceed.
Cards can only be evolved from their current rarity to the next highest rarity. Brackets mean virtual conversion rates, that are listed only for math's sake
|Common||50 to 5||(500 to 5)||(2,000 to 1)|
|Rare||-||50 to 5||(200 to 1)|
|Epic||-||-||20 to 1|
Here are some charts with all the possible evolutions, updated to Housekeeping event (2019-04-19). The sequence the cards are listed is roughly the same in which they appear on SQUAD tab.