This is a simple and fun level. If you went on a diversion in the first level, then you know what these green tiles indicate. When you step on one, it'll quickly vanish (about three or so seconds, maybe less?). Head across this first path, and long jump if you're in the mood to go quickly. Get the 1-Up Mushroom if you want then head onto the main, non-vanishing platform. Head left onto the vanishing platform and hit the ? block if you wish. Wait until the platform's completely vanished, drop down and shoot through the launch star.
You'll land on the main attraction - the satellite! Now, right away the platforms will start to vanish. You must get all of the music notes here in order to get the star. There are multiple different paths you can, and eventually you'll probably have to jump over gaps where platforms once were. Once you've gotten all of the music notes, jump down and get the star in the middle (don't worry - the black hole is gone now).