Saving

The game gives you the opportunity to save at two points:
 * You are in the temple
 * You are about to move on to the next forest level via a princessvine.

In the temple, you select the "Save" item from the transporter menu. In the forest, there is a "Save" option underneath "Go ahead" when you move levels.

Save Slots
The game unfortunately limits you to three save games per save file, and one save file per memory card.

The two main ways to get round this are:
 * Use multiple memory cards
 * Use a computer-to-memory card interface to backup your games, then overwrite your existing saves.