Whenever you see a tall springy pole (that you can vault yourself off of) vault off of it and land on the top of the pole. If done correctly, you'll bounce 10 times on the pole, and gain 1 extra life for each bounce. After that, die and repeat the process.
Note: The maximum amount you can get is 255 lives. If you go over 255, you will be taken back to 1 Life.
Near the end of Round 5-3 of "Cloud Paradise", get a running start on the cloud platforms, jump to the top of the Swing Pole, and swing yourself all the way to the top of the sky. If you time it just right, you will bump your head on a Trophy. Getting the Trophy will rewind the clock back an hour (1 Day of in-game time). This is perfect if you are aiming for the best ending, and you are below 1:00:00 of in-game time.
There are 5 possible endings in this game, depending on how much time you spent in the game.