I take it you have gotten as far as pressing START and are at the Load/Save screen?
Well...
1)  Unless already done so, click on SAVE (A button)
2)  Click on the save-number you want.  (A button again - It should highlight.)
3)  Hold down the RIGHT TRIGGER button.  Now moving the joystick will allow you to select the letter (Up/Down) or move the curson (Left/Right)...  Note - moving left will DELETE the character.
4)  Double click (A button) on the highlighted save number to save the game.
...  The game also auto-saves every now and then - The game may pause for about 10 seconds or so.