Act 1 is a straightforward introduction. Start by running right, collecting rings and jumping over small gaps. You'll encounter your first enemies, the Motobugs (red ladybug-like robots) and Buzz Bombers (flying bee robots). Destroy them with a jump or Spin Dash. Look for springs to launch you to higher platforms. There's a hidden 1-Up Monitor early on; after the first loop-de-loop, look for a spring that launches you upwards to a small platform. Continue right, navigating through more loops and slopes. The goal is a large signpost at the end of the level. Hit it to complete the Act.
Don't rush too much on your first playthrough; take some time to explore the different routes. There are many opportunities to collect rings and get a feel for Sonic's speed. After the first large loop, you can often find a lower path with a few rings and a shield monitor. Experiment with the Spin Dash to see how it helps you clear obstacles and gain speed quickly. This act is designed to teach you the ropes, so enjoy the ride!