Well, one option is to make sure your game settings have auto-save enabled. Also, remember to manually save at key points in the game to avoid losing progress. Another thing you can do is keep an eye on the game's prompts for saving opportunities.
To nap in Doraemon Story of Seasons, first, look for a place that seems relaxing. It could be a bench in a park or a hammock. Then, interact with that spot and select the 'nap' option if it's available. Remember, some areas might be more conducive to napping than others.