When you pass through the Red Ring at Point 1, eight red coins drop down from above you. Jump between the swiveling platforms to collect the coins as they approach.
The first Star Coin is hidden in a nook above Point 2. Locate the ledge at the top of the screen, then wait for the nearest set of Blocks to swivel into place.
Make a running leap up to the ledge, then hop up to grab the Star Coin.
The path splits just past the Checkpoint Flag. Each path contains one of the remaining Star Coins. If you wish to collect them both, enter the yellow pipe to search the underground passage before you explore the upper path.
Hit the ? Block at the start of the underground passage to collect a Gold Flower. Use your gold fireballs to blast a path to the Star Coin at Point 4.
When you return to the surface, move left to find the Star Coin at Point 5. Use the Note Blocks to bounce up to the lower set of Blocks, then jump over and collect the Star Coin.