To unlock Yoshi in Super Mario Run you need 30 Red Toads and 30 Yellow Toads from Toad Rally. You can use these Toads to unlock his house in the Special section of the Shop screen. Once you unlock his house and build it in your Kingdom he will be available to play.
Yoshi features a special Flutter jump. To utilize the Flutter jump just touch and hold you screen like you would to perform a high jump with Mario or Luigi.Click the link to learn how to earn and use Toad Tickets to compete in Toad Rally.