The first Star Coin is located under the platform at Point 1. Stomp the nearby Koopa and use its shell to clear away a few of the nearby Blocks. Wait for the toadstool to expand, then drop to it and crouch down. When the toadstool contracts, it carries you to the Star Coin.
When you pass through the Red Ring at Point 2, eight red coins appear in the area. As the surrounding platforms expand and contract, use them to reach each of the coins.
The second Star Coin is located in a hidden area. To find it, enter the yellow pipe at Point 3.
Dodge past the incoming fireballs and pass through the Gold Ring at the top of the room. Clear out the enemies, then collect the Star Coin near the right wall.
To collect the third Star Coin, you must find the passage hidden at Point 4. If you crossed the toadstools to reach this area, head back and climb up to the Blocks near the top of the screen. Dash to the right, then leap from the last Block to find the hidden passage.
When you reach the end of the passage, drop down and collect the Star Coin.