Zone 1-1
Zone 1-1 gives you more than enough time to complete the stage, but it's just an introduction to get used to Sonic using the spin-dash to get around.
Key 1
The first key can be found by walking all the way forward. A short spin-dash will do here, but watch out for enemies and other annoying obstacles. Also, behind the key to the left (not Sonic's left, your left) you can find a useful set of flickering triangles. Depending on the color, you'll get a different item. See the items and power-ups page for more information. When you see an orange spring, just walk into it and Sonic will bounce to the next piece of land. Here, there are the last two keys.
Key 2
The second key can be seen inside (or hovering over) an enemy. Spin-dash through the enemy to destroy it and get the key in time. If you don't, the enemy will respawn and you'll have to destroy it again. Try to do a small spin-dash when near it. If you end up going off-course, it'll be a little harder to get back to the key.
Key 3
The last key is very simply scattered to the right. After you obtain all three keys, Sonic will do a little dance. Now you can go to the goal since your exit isn't blocked anymore. Then a little "Congratulations, Zone Complete" screen will pop up, showing your stats (like the kilometers an hour you traveled) and you'll move on to Zone 1-2.
Zone 1-2
The second zone, you still have large amount of time to complete the stage. The second zone introduces new strategies and obstacles as well.
Key 1
The first key here should be located all the way down south. Just keep going straight ahead and try to avoid annoying obstacles (enemies and flippers). Try to snatch any chances for items along the way.
Key 2
The next key will be on a path up from springs. Just go up the huge glass ramp (a medium spin-dash or a lot of small spin-dashes will do. One that's too big will get you off track and ricocheting off the walls.) From here, go to your left and you'll see a spring. Just bounce on it and Sonic will work his way up from there.
Key 3
After making a stop for the second key, go the opposite direction to see a small ramp and the last key. After snatching it, go back to the springs (the place where you got the second key) and you should see a clear hole in the wall. Go through the hole to see the exit. If you missed a key, there's a spring leading back up, so all you have to worry about then is time. Get to the goal to complete the second zone in the Labyrinth of the Sky, leading you to the last zone. As a forewarning, after the Labyrinth of the Sky, things will be getting a little more hardcore.
Zone 1-3
Zone 1-3 is larger than the previous two, but easy to navigate as long as you know the layout of the map.
Key 1
The first key is located in the corner. From the starting location, climb up the first ramp, and head down and left. The key can be found on the lower corner.
Key 2
Head up and to the left for the second key. Destroy the monster carrying it, and grab it when it hits the ground.
Key 3
The third key is at the top of the map. It is located next to the set of four spikes.
Once you collect the third key, head to the goal, located just to the left. If you collected keys out of order, remember that the exit is located in the top-left area of the map.
Zone 1-4
The fourth zone is a long trip down a ramp, where you need to collect as many rings as possible; if you collect 100, then you get an extra life.
The rings appear in batches of six, and start at the left-hand side of the ramp. As you proceed down the ramp, the placement of the groups gradually moves to the right. If you can get at least 100 coins, you gain an extra life.
While not necessary at this zone, you can press 
or 
to brake.
The first boss has its minions appear in the center, and randomly choose a direction to walk in. After the minions all disappear, your main opponent enters. He will detach it's claws, which will fly in your general direction. They will re-attach to the main body, which will then teleport to the new location.
It can be defeated easily by a properly placed spin-dash. Your spin dash should bounce you back-and-forth over the boss, damaging it each time you cross over it.