Super Mario Run marks Mario's official debut on mobile platforms. Though the game may look and sound familiar for Mario fans, Mario's inexplicable desire to keep on running forward means you have less control over him in Super Mario Run than you do in more traditional Mario games.
Still, there's one element to Super Mario Run that should feel familiar to long-time fans of the series: You can play as different characters, each with their own strengths, weaknesses, and abilities (just make sure you're near an internet connection whenever you play). For example, the Princess can glide, Mario can take an extra hit if he grabs a Super Mushroom, and Yoshi can flutter-jump.
Most of Super Mario Run's characters are accessed through the Kingdom Builder's shop. In the Kingdom Builder, tap "Build," then "Shop," then tap the "Special" sub-category. These are items that give you access to special features, e.g. extra courses, bonus game huts, and the aforementioned extra characters.
You need two things to buy these characters: Lots of coins, and lots of Toad admirers of different colors. You can get both by playing Toad Rally. When selecting a course in Toad Rally, make sure the opponent you select will bring in the Toads you need (pay attention to the colors of the Toads next to each player's score).
When you have what you need, you can start unlocking characters' houses in the Kingdom Builder shop! Make sure you have a place to put their buildings. To change which character you want to play as, tap on the character icon beside the "Start" button when you select a level.
To unlock Mario -- Mario's the default character in Super Mario Run. Mario can find Mushrooms in question blocks, which let him grow big and take an extra hit from enemies.
To unlock Princess Peach -- Beat Super Mario Run's tour mode to rescue the Princess from Bowser. She'll be playable from thereon out.
To unlock Luigi -- You can build Luigi's house once you have 150 Green Toads and 150 Purple Toads in Kingdom Builder.
To unlock Toadette -- You can build Toadette's house once you have 200 Red Toads, 200 Blue Toads, and 200 Green Toads in Kingdom Builder.
To unlock Yoshi -- You can unlock Yoshi's house (it's an egg!) once you have 30 Red Toads and 30 Yellow Toads in Kingdom Builder. You also need to pay 1000 coins.