Street races are first unlocked after you complete your first green wristband event. These are different to Festival Events in that you race for large sums of money instead of wristband progression. The street race hubs will be indicated by a ‘money’ icon on your map and you will need to drive to the location marked.
Unlike festival races, street races will include traffic, so be sure to keep your eyes open and stick to the right side of the road is approaching a crest, as hitting a car could cost you first place. Also note that the tracks aren't closed off, meaning it's possible to miss a turn or side street, so pay close attention to your map and the blue spotlight/checkpoints. In street races the other racers will often cut corners and appear to be more aggressive than Festival races, so try and keep your distance if possible.
Each race you win will be marked with a ‘1st’ icon on the race ticket. Once you win 10 different street races the achievement will unlock. To make this easy, set AI difficulty to easy and turn on all assists.