Too save in Majora's Mask (Native Save), there's two options, and they are good and bad at different situations
1. Play the Song of Time (down A left down A left) What does it do?: This is the best type of save except when you're doing a dungeon, trading sequence, etc. You go back to the dawn of the First Day. You lose all of your event items, bottle contents, ammunition, dungeon progress, small keys, pictographs, razor sword, and boss key for all dungeons. If you lost your sword, you get it back (unless you had razor sword, then you get Kokiri Sword back)
2. Owl Statue What does it do?: It quits saves and quits your game temporarily. Open it up and you'll end up at the exact same spot with the exact same items and time you had when you saved. Be warned: if you quit without saving after going to an owl statue, you'll start back at the last time you played the Song of Time. This is good when you gotta quit when you are doing something that the song of time will make you loose.
3. It is a way to save. It counts, but it is only activated once in the file. Clock Town Save What does it do?: When you reach clocktown for the first time, you automatically save. It's like a regular save in a regular game. You keep all of your ammunition (only deku nuts at the time, sadly).
Update: 4. Beat the Game It is exactly the same thing as Clock Town Save except you have to beat the game. You get all of your masks back too.