Keys are the most important items in the game. Without them, you can't move on. Collect three of them to open the exit and move on to the next stage. When Sonic takes damage, the keys will scatter out. If Sonic doesn't recollect all of them quickly enough, they go back to their original spots, thus wasting time.
Rings don't appear in regular stages, but in other stages (boss or bonus stages) appear with the same role they always have in Sonic games--protecting Sonic from losing a life. 100 rings add to a 1up.
Power-ups appear differently then they do in other Sonic games--they now appear as triangles. Recognize the power-ups by their colors, and snatch it before it's too late.
Erases all enemies on screen. It doesn't have too much an effect, since enemies respawn quite quickly, but is still helpful when Sonic's robotic enemies are getting annoying.
A very helpful power-up, but, because of its high value to Sonic, appears less frequently than all other power-ups. Obviously, it gives Sonic an extra life without needing to collect the 100 rings.
It gives Sonic temporary invincibility. Similar to the invincibility item boxes from the main series, just with a different name. When running into enemies, they are destroyed, and is also invincible to enemy attacks.
May be Sonic's last hope for his trademark speed in the labyrinth. Run around like it's a normal top-down Sonic 8-bit title, without needing the spin-dash. The triangles being blue might have to do with referencing Sonic's speed.
Time is just another one of Sonic's enemies in the labyrinth. When time is running out and you still need to collect some keys or reach the exit, the Magic Clock is a big help.