You can only do a temporary save in battle. The reason being SE knew it was a handheld game, and people play handheld games at times when they're going to have to turn the game off at a moment's notice. To do it, hit B until it takes you to the "free look pointer" (my name for the mode where you can use the cursor to look at different units, but not much else. Then press select. A menu with options to check the laws will come up. One of the options on the list is "save now".

To save on the map, just hit start. It'll bring up a menu and save will be on there.