The Hero side is the story of the three playable "Good" characters, Sonic, Tails, and Knuckles, as well as the non-playable Amy Rose (who still has a major role in the story.) and their struggle to stop Eggman, who is once again trying to take over the world. It begins with a cutscene of Sonic, being held prisoner in an aircraft, who suddenly breaks out and leaps through a door into the air. He grabs a metal board and begins riding. After this video, the playable levels begin.
City Escape (Speed)
This first level starts out exactly where the cutscene leaves off, with Sonic falling out of the sky on his makeshift board. After a few seconds, he hits the streets of what looks to be San Francisco, and starts "snowboarding" down the hills. During this sequence, pressing the 
button will cause Sonic to brake, while the other controls act as normal. Cars appear on the street as obstacles, and running into them will cause Sonic to slow down as well. Additionally, ramps will appear as you move down the hill, and by performing a trick off of them at the right moment, you can score lots of points and potentially hit a few high-flying item boxes. As you descend down the hill, the cue that this sequence is going to end is a trolley. It's practically unavoidable, so just ram into it. After this, you'll lose the board and begin the regular portion of the level.
Once you land, start moving to the left. There's a save point nearby, so be sure to hit so you won't have to go through the boarding part again.