After completing a battle in either Z Campaign(Story) or SP Battle (ranking) you are given standings, in Z Campaign you are given a rank, the lower the number the better. In SP battle you are judged in these catagories:

Time to complete the current battle
Total time in battle so far
Number of characters killed in the current battle(your team)
Total number of characters killed so far(your team)

From this standings screen, press a button to get to the Save screen. On this screen you can choose from the following:

Continue but do not save
File 1
File 2
File 3

Press the accept button when you have highlighted your choice. It will now ask you if you want to do what you selected. Yes is the first choice, no is the second.